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physics
oscillations mechanical waves

Questions and Answers of Oscillations Mechanical Waves

An LC oscillator consists of a 2.00nF capacitor and a 2.00 mH inductor. The maximum voltage is 4.00 V. What are?(a) The frequency of the oscillations,(b) The maximum current,(c) The maximum energy
Figure shows an RLC circuit that is driven by an emf source of fixed amplitude ξ m. Initially the circuit consists of one resistor of resistance R. one inductor of inductance L, and one capacitor of
Can the acceleration and the displacement of a simple harmonic oscillator ever be in the same direction? The acceleration and the velocity? The velocity and the displacement? Explain.
The position of a particle is given by x = (7 cm) x cos 6πt, where t is in seconds. What is?(a) The frequency,(b) The period,(c) The amplitude of the particle's motion?(d) What is the first time
(a) What is the maximum speed of the particle in Problem 6?(b) What is its maximum acceleration?
What is the phase constant d in Equation 14-4 if the position of the oscillating particle at time t = 0 is (a) 0, (b) A, (c) A, (d) A/2?
A particle of mass m begins at rest from x = +25 cm and oscillates about its equilibrium position at x = 0 with a period of 1.5 s. Write equations for(a) The position x versus the time t,(b) The
Find(a) The maximum speed,(b) The maximum acceleration of the particle in Problem 6.(c) What is the first time that the particle is at x = 0 and moving to the right?
Work Problem 9 with the particle initially at x = 25 cm and moving with velocity v0 = +50 cm/s.
The period of an oscillating particle is 8 s, and its amplitude is 12 cm. At t = 0, it is at its equilibrium position. Find the distance traveled during the interval(a) t = 0 to t = 2 s,(b) t = 2 s
The period of an oscillating particle is 8 s. At t = 0, the particle is at rest at x = A = 10 cm.(a) Sketch x as a function of t.(b) Find the distance traveled in the first second, the next second,
Military specifications often call for electronic devices to be able to withstand accelerations of 10g = 98.1 m/s2. To make sure that their products meet this specification, manufacturers test them
The position of a particle is given by x = 2.5 cos pt, where x is in meters and t is in seconds.(a) Find the maximum speed and maximum acceleration of the particle.(b) Find the speed and acceleration
The bow of a destroyer undergoes a simple harmonic vertical pitching motion with a period of 8.0 s and an amplitude of 2.0 m.(a) What is the maximum vertical velocity of the destroyer’s bow?(b)
A particle moves in a circle of radius 40 cm with a constant speed of 80 cm/s. Find(a) The frequency of the motion,(b) The period of the motion.(c) Write an equation for the x component of the
A particle moves in a circle of radius 15 cm, making 1 revolution every 3 s.(a) What is the speed of the particle?(b) What is its angular velocity w?(c) Write an equation for the x component of the
A 2.4-kg object is attached to a horizontal spring of force constant k = 4.5kN/m. The spring is stretched 10 cm from equilibrium and released. Find its total energy.
Find the total energy of a 3-kg object oscillating on a horizontal spring with an amplitude of 10 cm and a frequency of 2.4 Hz.
A 1.5-kg object oscillates with simple harmonic motion on a spring of force constant k = 500 N/m. Its maximum speed is 70 cm/s.(a) What is the total energy?(b) What is the amplitude of the
A 3-kg object oscillating on a spring of force constant 2kN/m has a total energy of 0.9 J.(a) What is the amplitude of the motion?(b) What is the maximum speed?
An object oscillates on a spring with an amplitude of 4.5 cm. Its total energy is 1.4 J. What is the force constant of the spring?
A 3-kg object oscillates on a spring with an amplitude of 8 cm. Its maximum acceleration is 3.50 m/s2. Find the total energy.
A 2.4-kg object is attached to a horizontal spring of force constant k = 4.5kN/m. The spring is stretched 10 cm from equilibrium and released. Find(a) The frequency of the motion,(b) The period,(c)
Answer the questions in Problem 29 for a 5-kg object attached to a spring of force constant k = 700 N/m when the spring is initially stretched 8 cm from equilibrium.
A 3-kg object attached to a horizontal spring oscillates with an amplitude A = 10 cm and a frequency f = 2.4 Hz.(a) What is the force constant of the spring?(b) What is the period of the motion?(c)
An 85-kg person steps into a car of mass 2400 kg, causing it to sink 2.35 cm on its springs. Assuming no damping, with what frequency will the car and passenger vibrate on the springs?
A 4.5-kg object oscillates on a horizontal spring with an amplitude of 3.8 cm. Its maximum acceleration is 26 m/s2. Find(a) The force constant k,(b) The frequency, and(c) The period of the motion.
An object oscillates with an amplitude of 5.8 cm on a horizontal spring of force constant 1.8kN/m. Its maximum speed is 2.20 m/s. Find(a) The mass of the object,(b) The frequency of the motion,
A 0.4-kg block attached to a spring of force constant 12 N/m oscillates with an amplitude of 8 cm. Find(a) The maximum speed of the block,(b) The speed and acceleration of the block when it is at x =
An object of mass m is supported by a vertical spring of force constant 1800 N/m. When pulled down 2.5 cm from equilibrium and released from rest, the object oscillates at 5.5 Hz.(a) Find m.(b) Find
An object of unknown mass is hung on the end of an unstretched spring and is released from rest. If the object falls 3.42 cm before first coming to rest, find the period of the motion.
A spring of force constant k = 250 N/m is suspended from a rigid support. An object of mass 1 kg is attached to the unstretched spring and the object is released from rest.(a) How far below the
The St. Louis Arch has a height of 192 m. Suppose a stunt woman of mass 60 kg jumps off the top of the arch with an elastic band attached to her feet. She reaches the ground at zero speed. Find her
A 0.12-kg block is suspended from a spring. When a small stone of mass 30 g is placed on the block, the spring stretches an additional 5 cm. With the stone on the block, the spring oscillates with an
In Problem 40, find the maximum amplitude of oscillation such that the stone will remain on the block. To remain on the block, the block’s maximum downward acceleration must not exceed g.
An object of mass 2.0 kg is attached to the top of a vertical spring that is anchored to the floor. The uncompressed length of the spring is 8.0 cm, and the equilibrium position of the object on the
Lou has devised a new kiddie ride and is testing it for safety. A child is placed on a large block that is attached to a horizontal spring. When pulled back and released, the child and block
A 2.5-kg object hanging from a vertical spring of force constant 600 N/m oscillates with an amplitude of 3 cm. When the object is at its maximum downward displacement, find(a) The total energy of the
A 1.5-kg object that stretches a spring 2.8 cm from its natural length when hanging at rest oscillates with an amplitude of 2.2 cm.(a) Find the total energy of the system.(b) Find the gravitational
A 1.2-kg object hanging from a spring of force constant 300 N/m oscillates with a maximum speed of 30 cm/s.(a) What is its maximum displacement? When the object is at its maximum displacement,
The length of the string or wire supporting a pendulum increases slightly when its temperature is raised. How would this affect a clock operated by a simple pendulum?
Find the length of a simple pendulum if the period is 5 s at a point where g = 9.81 m/s2.
What would be the period of the pendulum in Problem 50 if the pendulum were on the moon, where the acceleration due to gravity is one-sixth that on earth?
If the period of a pendulum 70 cm long is 1.68 s, what is the value of g at the location of the pendulum?
A pendulum set up in the stairwell of a 10-story building consists of a heavy weight suspended on a 34.0-m wire. If g = 9.81 m/s2, what is the period of oscillation?
A simple pendulum of length L is attached to a cart that slides without friction down a plane inclined at angle ? with the horizontal as shown (Figure). Find the period of oscillation of the pendulum
A simple pendulum of length L is released from rest from an angle f0.(a) Assuming that the pendulum undergoes simple harmonic motion, find its speed as it passes through f = 0.(b) Using the
A thin disk of mass 5 kg and radius 20 cm is suspended by a horizontal axis perpendicular to the disk through its rim. The disk is displaced slightly from equilibrium and released. Find the period of
A circular hoop of radius 50 cm is hung on a narrow horizontal rod and allowed to swing in the plane of the hoop. What is the period of its oscillation, assuming that the amplitude is small?
A 3-kg plane figure is suspended at a point 10 cm from its center of mass. When it is oscillating with small amplitude, the period of oscillation is 2.6 s. Find the moment of inertia I about an axis
Figure shows a dumbbell with two equal masses (to be considered as point masses) attached to a very thin (massless) rod of length L. (a) Show that the period of this pendulum is a minimum when the
Suppose the rod in Problem 60 has a mass of 2m (Figure). Determine the distance between the upper mass and the pivot point P such that the period of this physical pendulum is a minimum.
You are given a meter stick and asked to drill a hole in it so that when pivoted about the hole the period of the pendulum will be a minimum. Where should you drill the hole?
An irregularly shaped plane object of mass 3.2 kg is suspended by a thin rod of adjustable length and is free to swing in the plane of the object (Figure). When the length of the supporting rod is
When a short person and a tall person walk together at the same speed, the short person will take more steps. Consider the leg to be a physical pendulum that swings about the hip joint. Estimate the
Figure shows a uniform disk of radius R = 0.8 m and a 6-kg mass with a small hole a distance d from the disk’s center that can serve as a pivot point.(a) What should be the distance d so that
A plane object has moment of inertia I about its center of mass. When pivoted at point P1, as shown in Figure 14-33, it oscillates about the pivot with a period T. There is a second point P2 on the
A physical pendulum consists of a spherical bob of radius r and mass m suspended from a string (Figure). The distance from the center of the sphere to the point of support is L. When r is much less
Figure shows the pendulum of a clock. The uniform rod of length L = 2.0 m has a mass m = 0.8 kg. Attached to the rod is a disk of mass M = 1.2 kg and radius 0.15 m. The clock is constructed to keep
A pendulum clock loses 48 s per day when the amplitude of the pendulum is 8.4o. What should be the amplitude of the pendulum so that the clock keeps perfect time?
A pendulum clock that has run down to a very small amplitude gains 5 min each day. What angular amplitude should the pendulum have to keep the correct time?
An oscillator has a Q factor of 200. By what percentage does its energy decrease during one period?
A 2-kg object oscillates with an initial amplitude of 3 cm on a spring of force constant k = 400 N/m. Find(a) The period, and(b) The total initial energy.(c) If the energy decreases by 1% per period,
Show that the ratio of the amplitudes for two successive oscillations is constant for a damped oscillator.
An oscillator has a period of 3 s. Its amplitude decreases by 5% during each cycle.(a) By how much does its energy decrease during each cycle?(b) What is the time constant τ?(c) What is the Q factor?
An oscillator has a Q factor of 20.(a) By what fraction does the energy decrease during each cycle?(b) Use Equation 14-35 to find the percentage difference between w’ and w0.
For a child on a swing, the amplitude drops by a factor of 1/e in about eight periods if no energy is fed in. Estimate the Q factor for this system.
A damped mass–spring system oscillates at 200 Hz. The time constant of the system is 2.0 s. At t = 0, the amplitude of oscillation is 6.0 cm and the energy of the oscillating system is then 60
It has been stated that the vibrating earth has a resonance period of 54 min and a Q factor of about 400 and that after a large earthquake, the earth “rings” (continues to vibrate) for about 2
A 3-kg sphere dropped through air has a terminal speed of 25 m/s. (Assume that the drag force is – bv.) Now suppose the sphere is attached to a spring of force constant k = 400 N/m and that it
Find the resonance frequency for each of the three systems shown in Figure 14-36.
A damped oscillator loses 2% of its energy during each cycle.(a) What is its Q factor?(b) If its resonance frequency is 300 Hz, what is the width of the resonance curve ∆w when the oscillator
A 2-kg object oscillates on a spring of force constant k = 400 N/m. The damping constant has a value of b = 2.00 kg/s. The system is driven by a sinusoidal force of maximum value 10 N and angular
A damped oscillator loses 3.5% of its energy during each cycle.(a) How many cycles elapse before half of its original energy is dissipated?(b) What is its Q factor?(c) If the natural frequency is 100
Tarzan is depressed again. He ties a vine to his ankle and swings upside-down with a period of 3s as he contemplates his troubles. Cheetah the chimpanzee pushes him so that the amplitude remains
Peter lays his jack-in-the-box on its side with the lid open, so that Jack, a painted 0.4-kg clown, sticks out horizontally at the end of a spring. Peter then takes a 0.6-kg wad of putty, places it
Figure shows a vibrating mass-spring system supported on a frictionless surface and a second equal mass that is moving toward the vibrating mass with velocity v. The motion of the vibrating mass is
Following the elastic collision in Problem 93, the energy of the recoiling mass is 8.0 J. Find the masses m and the spring constant k.
An object of mass 2 kg resting on a frictionless horizontal surface is attached to a spring of force constant 600 N/m. A second object of mass 1 kg slides along the surface toward the first object at
A particle has a displacement x = 0.4 cos(3t + p/4), where x is in meters and t is in seconds.(a) Find the frequency f and period T of the motion.(b) Where is the particle at t = 0?(c) Where is the
(a) Find an expression for the velocity of the particle whose position is given in Problem 102.(b) What is the velocity at time t = 0?(c) What is the maximum velocity?(d) At what time after t =
An object on a horizontal spring oscillates with a period of 4.5s. If the object is suspended from the spring vertically, by how much is the spring stretched from its natural length when the object
A small particle of mass m slides without friction in a spherical bowl of radius r. (a) Show that the motion of the particle is the same as if it were attached to a string of length r. (b) Figure
As your jet plane speeds down the runway on take-off, you measure its acceleration by suspending your yo-yo as a simple pendulum and noting that when the bob (mass 40 g) is at rest relative to you,
Two identical blocks placed one on top of the other rest on a frictionless horizontal air track. The lower block is attached to a spring of spring constant k = 600 N/m. When displaced slightly from
Two atoms are bound together in a molecule. The potential energy U resulting from their interaction is shown in Figure. The variable r is the distance between the atom centers, and E0 is the lowest
A wooden cube with edge a and mass m floats in water with one of its faces parallel to the water surface. The density of the water is r. Find the period of oscillation in the vertical direction if it
A spider of mass 0.36 g sits in the middle of its horizontal web, which sags 3.00 mm under its weight. Estimate the frequency of vertical vibration for this system.
A clock with a pendulum keeps perfect time on the earth’s surface. In which case will the error be greater: if the clock is placed in a mine of depth h or if the clock is elevated to a height h?
Figure shows a pendulum of length L with a bob of mass M. The bob is attached to a spring of spring constant k as shown. When the bob is directly below the pendulum support, the spring is
An object of mass m1 sliding on a frictionless horizontal surface is attached to a spring of force constant k and oscillates with an amplitude A. When the spring is at its greatest extension and the
The acceleration due to gravity g varies with geographical location because of the earth’s rotation and because the earth is not exactly spherical. This was first discovered in the seventeenth
Figure shows two equal masses of 0.6 kg glued to each other and connected to a spring of spring constant k = 240 N/m. The masses, which rest on a frictionless horizontal surface, are displaced 0.6 m
Show that for the situations in Figures a and b, the object oscillates with a frequency f = [1/(2π)] √keff/m, where keff is given by(a) keff = k1 + k2 and(b) 1/keff = 1/k1 + 1/k2.
A small block of mass m1 rests on a piston that is vibrating vertically with simple harmonic motion given by y = A sin wt.(a) Show that the block will leave the piston if w2A > g.(b) If w2A = 3g
The plunger of a pinball machine has mass mp and is attached to a spring of force constant k (Figure). The spring is compressed a distance x0 from its equilibrium position x = 0 and released. A ball
A level platform vibrates horizontally with simple harmonic motion with a period of 0.8 s.(a) A box on the platform starts to slide when the amplitude of vibration reaches 40 cm; what is the
The potential energy of a mass m as a function of position is given by U(x) = U0(a + 1/a), where a = x/a and a is a constant.(a) Plot U(x) versus x for 0.1a < x <
Repeat Problem 120 with U(x) = U0(a2 + 1/a2).
A solid cylindrical drum of mass 6.0 kg and diameter 0.06 m rolls without slipping on a horizontal surface (Figure). The axle of the drum is attached to a spring of spring constant k = 4000 N/m as

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