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physics
oscillations mechanical waves

Questions and Answers of Oscillations Mechanical Waves

What is the phase constant for the harmonic oscillator with the velocity function v(t) given in Figure if the position function x(t) has the form x = x- cos (wt + Φ)? The vertical axis scale is set
In Figure two identical springs of spring constant 7580 N/m are attached to a block of mass 0.245 kg. What is the frequency of oscillation on the friction-less floor?
Figure shows block 1 of mass 0.200 kg sliding to the right over a frictionless elevated surface at a speed of 8.00 m/s. The block undergoes an elastic collision with stationary block 2, which is
An oscillator consists of a block attached to a spring (k = 400 N/m). At some time t, the position (measured from the system's equilibrium location), velocity, and acceleration of the block are x =
At a certain harbor, the tides cause the ocean surface to rise and fall a distanc e d (from highest level to lowest level) in simple harmonic motion, with a period of I2.5 h. How long does it take
A block is on a horizontal surface (a shake table) that is moving back and forth horizontally with simple harmonic motion of frequency 2.0 Hz. The coefficient of static friction between block and
Two particles execute simple harmonic motion of the same amplitude and frequency along close parallel lines. They pass each other moving in opposite directions each time their displacement is half
Two particles oscillate in simple harmonic motion along a conrmon straight-line segment of length A. Each particle has a period of 1.5 s, but they differ in phase by π/6 rad.(a) How far apart are
Figure a is a partial graph of the position function x(t) for a simple harmonic oscillator with an angular frequency of 1.20 rad/s; Figure b is a partial graph of the corresponding velocity function
A block rides on a piston that is moving vertically with simple harmonic motion.(a) If the SHM has period 1.0 s, at what amplitude of motion will the block and piston separate?(b) If the piston has
A simple harmonic oscillator consists of a block of mass 2.00 kg attached to a spring of spring constant 100 N/m. When t = 1.00 s, the position and velocity of the block are x = 0.129 m and v = 3.415
In Figure two springs are attached to a block that can oscillate over a frictionless floor. If the left spring is removed, the block oscillates at a frequency of 30 Hz. If, instead, the spring on the
In Figure two blocks (m = 1.8kg and M = 10 kg) and a spring (k = 200 N/m) are arranged on a horizontal, frictionless surface. The coefficient of static friction between the two blocks is 0.40. What
In Figure a block weighing 14.0 N, which can slide without friction on an incline at angle θ = 40.0o, is connected to the top of the incline by a massless spring of unstretched length 0.450 m and
In Figure two springs are joined and connected to a block of mass 0.245 kg that is set oscillating over a frictionless floor. The springs each have spring constant k = 6430 N/m. What is the frequency
Find the mechanical energy of a block-spring system having a spring constant of 1.3 N/cm and an oscillation amplitude of 2.4 cm.
An oscillating block-spring system has a mechanical energy of 1.00J, an amplitude of 10.0 cffi, and a maximum speed of 1 .20 mls. Find(a) The spring constant,(b) The mass of the block, and(c) The
When the displacement in SHM is one-half the amplitude xm, what fraction of the total energy is(a) Kinetic energy and(b) Potential energy?(c) At what displacement, in terms of the amplitude, is the
Figure gives the one-dimensional potential energy well for a 2.0 kg particle (the function U(x) has the form bx2 and the vertical axis scale is set by us = 2.0 J). (a) If the particle passes through
A 5.00 kg object on a horizontal frictionless surface is attached to a spring with k = 1000N/m. The object is displaced from equilibrium 50.0 cm horizontally and given an initial velocity of 10.0 m/s
Figure shows the kinetic energy K of a simple harmonic oscillator versus its position x. The vertical axis scale is set by Ks = 4.0 J. What is the spring constant?
A 10 g particle undergoes SHM with an amplitude of 2.0mm, a maximum acceleration of magnitude 8.0 x 103 m/s2, and an unknown phase constant Φ. What are?(a) The period of the motion,(b) The maximum
If the phase angle for a block-spring system in SHM is π/6 rad and the block's position is given by x = xm cos (wt + Φ), what is the ratio of the kinetic energy to the potential energy at time t =
A block of mass M = 5.4 kg, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k = 6000 N/m. A bullet of mass m = 9.5g and velocity i of magnitude 630
In Figure block 2 of mass 2.0 kg oscillates on the end of a spring in SHM with a period of 20ms. The position of the block is given by x = (1.0 cm) cos (wt + ?/2). Block 1 of mass 4.0 kg slides
A mass less spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position yi such that the spring is at its rest length. The object
A 95 kg solid sphere with a 15 cm radius is suspended by a vertical wire. A torque of 0.20N ∙ m is required to rotate the sphere through an angle of 0.85 rad and then maintain that orientation.
The balance wheel of an old-fashioned watch oscillates with angular amplitude π rad and period 0.500s. Find (a) The maximum angular speed of the wheel, (b) The angular speed at displacement
Suppose that a simple pendulum consists of a small 60.0 g bob at the end of a cord of negligible mass. If the angle θ between the cord and the vertical is given by θ = (0.0800 rad) cos [(4.43
(a) If the physical pendulum of Sample Problem is inverted and suspended at point P, what is its period of oscillation?(b) Is the period now greater than, less than, or equal to its previous value?
In Sample Problem we saw that a physical pendulum has a center of oscillation at distance 2L/3 from its point of suspension. Show that the distance between the point of suspension and the center of
In Figure the pendulum with radius r = 10.0 cm and mass 500 g attached to a uniform rod with length L = 500 mm and mass 270 g.(a) Calculate the rotational inertia of the pendulum about the pivot
A physical pendulum consists of a meter stick that is pivoted at a small hole drilled through the stick a distance d from the 50 cm mark. The period of oscillation is 2.5s. Find d.
In Figure a physical pendulum consists of a uniform solid disk (of radius R = 2.35 cm) supported in a vertical plane by a pivot located a distance d = 1.75 cm from the center of the disk. The disk is
A physical pendulum consists of two meter-long sticks joined together as shown in Figure. What is the pendulum's period of oscillation about a pin inserted through point A at the center of the
A performer seated on a trapeze is swinging back and forth with a period of 8.85 s. If she stands up, thus raising the center of mass of the trapeze + performer system by 35.0cm, what will be the new
A thin uniform rod (mass = 0.50 kg) swings about an axis that passes through one end of the rod and is perpendicular to the plane of the swing. The rod swings with a period of 1.5 s and an angular
In Figure a stick of length L = 1.85m oscillates as a physical pendulum.(a) What value of distance x between the stick's center of mass and its pivot point O gives the least period?(b) What is that
The 3.00 kg cube in Figure has edge lengths d = 6.00 cm and is mounted on an axle through its center. A spring (k = 1200N/m) connects the cube's upper corner to a rigid wall. Initially the spring is
In the overhead view of Figure a long uniform rod of mass 0.600 kg is free to rotate in a horizontal plane about a vertical axis through its center. A spring with force constant k = 1850 N/m is
A rectangular block, with face lengths a = 35 cm and b = 45cm, is to be suspended on a thin horizontal rod running through a narrow hole in the block. The block is then to be set swinging about the
The angle of the pendulum of Figure b is given by θ = θm cos [(4.44 rad/s)t + Φ]. If at t = 0, 9 = 0.040rad and dθ/dt = 0.200 rad/s, what are (a) The phase constant Φ and (b) The
In Figure a, a metal plate is mounted on an axle through its center of mass. A spring with k = 2000 N/m connects a wall with a point on the rim a distance r = 2.5 cm from the center of mass.
A pendulum is formed by pivoting a long thin rod about a point on the rod. In a series of experiments, the period is measured as a function of the distance x between the pivot point and the rod's
In Figure a 2.50 kg disk of diameter D = 42.0 cm is supported by a rod of length L = 76.0 cm and negligible mass that is pivoted at its end.(a) With the massless torsion spring unconnected, what is
In Figure the block has a mass of 1.50 kg and the spring constant is 8.00 N/m. The damping force is given by – b(dx/dt), where b = 230 g/s. The block is pulled down 12.0 cm and released. (a)
In Sample Problem what is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles?
The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?
The suspension system of a 2000 kg automobile "sags" L0 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 50% each cycle. Estimate the values of (a) The spring
For Equation suppose the amplitude Fm is given by where F^ is the (constant) amplitude of the external oscillating force exerted on the spring by the rigid support in Figure. At resonance, what are
A 1000 kg car carrying four 32kg people travels over a "washboard" dirt road with corrugations 4.0 m apart. The car bounces with maximum amplitude when its speed is 16 km/h. When the car stops, and
A block is in SHM on the end of a spring, with position given by x = xm cos (wt + Φ). If Φ = π/5 rad, then at t = 0 what percentage of the total mechanical energy is potential energy?
Figure gives the position of a 20 g block oscillating in SHM on the end of a spring. The horizontal axis scale is set by ts = 40.0ms. What are?(a) The maximum kinetic energy of the block and(b) The
Figure gives the position x(t) of a block oscillating in SHM on the end of a spring (ts = 40.0 ms).What are(a) The speed and(b) The magnitude of the radial acceleration of a particle in the
Figure shows the kinetic energy K of a simple pendulum versus its angle θ from the vertical. The vertical axis scale is set by Ks = 10.0mJ. The pendulum bob has mass 0.200 kg. What is the length
Although California is known for earthquakes, it has large regions dotted with precariously balanced rocks that would be easily toppled by even a mild earthquake. The rocks have stood this way for
A 4.00 kg block is suspended from a spring with k = 500 N/m. A 50.0 g bullet is fired into the block from directly below with a speed of 150 m/s and becomes embedded in the block. (a) Find the
A 55.0 g block oscillates in SHM on the end of a spring with k = 1500 N/m according to x = xm cos (wt + Φ). How long does the block take to move from position + 0.800xm to (a) Position +
A loudspeaker diaphragm is oscillating in simple harmonic motion with a frequency of 440 Hz and a maximum displacement of 0.75 mm. What are the (a) Angular frequency, (b) Maximum speed, and (c)
The tip of one prong of a tuning fork undergoes SHM of frequency 1000 Hz and amplitude 0.40 mm. For this tip, what is the magnitude of the (a) Maximum acceleration, (b) Maximum velocity,(c)
A flat uniform circular disk has a mass of 3.00 kg and a radius of 70.0 cm. It is suspended in a horizontal plane by a vertical wire attached to its center. If the disk is rotated 2.50 rad about the
A uniform circular disk whose radius R is 12.6 cm is suspended as a physical pendulum from a point on its rim.(a) What is its period? (b) At what radial distance r < R is there a pivot point that
What is the frequency of a simple pendulum 2.0 m long(a) In a room, (b) In an elevator accelerating upward at a rate of 2.0 m/s2, and (c) In free fall?
A particle executes linear SHM with frequency 0.25 Hz about the point x = 0. At t = 0, it has displacement x = 0.37 cm and zero velocity. For the motion, determine the(a) Period, (b) Angular
A 50.0 g stone is attached to the bottom of a vertical spring and set vibrating. If the maximum speed of the stone is 15.0 cm/s and the period is 0.500 s, find the (a) Spring constant of the spring,
A 2.00 kg block hangs from a spring. A 300 g body hung below the block stretches the spring 2.00 cm farther. (a) What is the spring constant? (b) If the 300 g body is removed and the block is set
The end point of a spring oscillates with a period of 2.0 s when a block with mass m is attached to it. When this mass is increased by 2.0 kg, the period is found to be 3.0 s. Find m.
A 0.10 kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by x = (10 cm) cos [(10 rad/s)t + π/2 rad]. (a)
A 3.0 kg particle is in simple harmonic motion in one dimension and moves according to the equation x = (5.0 m) cos [(π/3 rad/s)t – π/4 rad], with / in seconds. (a) At what value of x
A mass less spring with spring constant 19 N/m hangs vertically. A body of mass 0.20 kg is attached to its free end and then released. Assume that the spring was un-stretched before the body was
The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 0.76 m. If the piston moves with simple harmonic motion with an angular frequency of 180rev/min, what is its
A wheel is free to rotate about its fixed axle. A spring is attached to one of its spokes a distance r from the axle, as shown in Figure.(a) Assuming that the wheel is a hoop of mass m and radius R,
The scale of a spring balance that reads from 0 to 15.0 kg is 12.0 cm long. A package suspended from the balance is found to oscillate vertically with a frequency of. 2.00 Hz(a) What is the spring
A uniform spring with k = 8600 N/m is cut into pieces I and 2 of un-stretched lengths L1 = 7.0 cm and L2 = 10 cm. What are? (a) k1 and (b) k2? A block attached to the original spring as in Figure
In Figure three 10 000 kg ore cars are held at rest on a mine railway using a cable that is parallel to the rails, which are inclined at angle θ = 30o. The cable stretches 15 cm just before the
A simple pendulum of length 20 cm and mass 5.0 g is suspended in a race car traveling with constant speed 70 m/s around a circle of radius 50 m. If the pendulum undergoes small oscillations in a
A vertical spring stretches 9.6 cm when a 1.3 kg block is hung from its end. (a) Calculate the spring constant. This block is then displaced an additional 5.0 cm downward and released from rest. Find
A block weighing 20 N oscillates at one end of a vertical spring for which k = 100 N/m; the other end of the spring is attached to a ceiling. At a certain instant the spring is stretched 0.30 m
A 1.2kg block sliding on a horizontal frictionless surface is attached to a horizontal spring with k = 480 N ∙ m. Let x be the displacement of the block from the position at which the spring is
A simple harmonic oscillator consists of an 0.80 kg block attached to a spring (k = 200 N/m).The block slides on a horizontal frictionless surface about the equilibrium point x = 0 with a total
An engineer has an odd-shaped 10 kg object and needs to find its rotational inertia about an axis through its center of mass. The object is supported on a wire stretched along the desired axis. The
A grandfather clock has a pendulum that consists of a thin brass disk of radius r = 15.00 cm and mass 1.000 kg that is attached to a long thin rod of negligible mass. The pendulum swings freely about
A block sliding on a horizontal frictionless surface is attached to a horizontal spring with a spring constant of 600 N/m. The block executes SHM about its equilibrium position with a period of 0.40
When a 20 N can is hung from the bottom of a vertical spring, it causes the spring to stretch 20 cm. (a) What is the spring constant? (b) This spring is now placed horizontally on a frictionless
A 4.00 kg block hangs from a spring, extending it 16.0 cm from its un-stretched position. (a) What is the spring constant?(b) The block is removed, and a 0.500 kg body is hung from the same spring.
A damped harmonic oscillator consists of a block (m = 2.00 kg), a spring (k = 10.0 N/m), and a damping force (F = – bv). Initially, it oscillates with an amplitude of 25.0 cm; because of the
A common device for entertaining a toddler is a jump seat that hangs from the horizontal portion of a doorframe via elastic cords (Figure). Assume that only one cord is on each side in spite of the
What is the phase constant for SMH with a(t) given in Figure if the position function x(t) has the form x = xm cos(wf + ?) and as = 4.0 m/s2?
A torsion pendulum consists of a metal disk with a wire running through its center and soldered in place. The wire is mounted vertically on clamps and pulled taut. Figure a gives the magnitude ? of
A spider can tell when its web has captured, say, a fly because the fly's thrashing causes the web threads to oscillate. A spider can even determine the size of the fly by the frequency of the
For a simple pendulum, find the angular amplitude θm at which the restoring torque required for simple harmonic motion deviates from the actual restoring torque by 1.0%. (See "Trigonometric
A simple harmonic oscillator consists of a block attached to a spring with k = 200 N/m. The block slides on a frictionless surface, with equilibrium point x = 0 and amplitude 0.20 m. A graph of the
A simple harmonic oscillator consists of a 0.50 kg block attached to a spring. The block slides back and forth along a straight line on a frictionless surface with equilibrium point x = 0. At t = 0
In Figure a solid cylinder attached to a horizontal spring (k = 3.00 N/m) rolls without slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.250
A block weighing 10.0 N is attached to the lower end of a vertical spring (k = 200.0 N/m), the other end of which is attached to a ceiling. The block oscillates vertically and has a kinetic energy of
A2.0 kg block executes SHM while attached to a horizontal spring of spring constant 200N/m. The maximum speed of the block as it slides on a horizontal frictionless surface is 3.0m/s what are? (a)
The vibration frequencies of atoms in solids at normal temperatures are of the order of 1013 Hz. Imagine the atoms to be connected to one another by springs. Suppose that a single silver atom in a
In Figure a 2500 kg demolition ball swings from the end of a crane. The length of the swinging segment of cable is 17 m. (a) Find the period of the swinging, assuming that the system can be treated
The center of oscillation of a physical pendulum has this interesting property: If an impulse (assumed horizontal and in the plane of oscillation) acts at the center of oscillation, no oscillations
A 2.0 kg block is attached to the end of a spring with a spring constant of 350 N/m and forced to oscillate by an applied force F = (15 N) sin (wdt), where wd = 35 rad/s. The damping constant is b =

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