Question: 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

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 at its equilibrium length.

(a) Derive an expression for the period of this oscillating system for small amplitude vibrations.

(b) Suppose that M = 1 kg and L is such that in the absence of the spring the period is 2.0 s. What is the spring constant k if the period of the oscillating system is 1.0 s?

Step by Step Solution

★★★★★

3.51 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a For small displacements ML d 2 dt 2 Mg kL Mg kL ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

10-P-O-O-W (311).docx

120 KBs Word File

Students Have Also Explored These Related Oscillations Mechanical Waves Questions!

Sunita Menon was sitting at her desk considering a perplexing problem. She was supposed to meet with Shirish Ratnaparkhi, her operations manager at A-CAT Corp., and discuss her ideas for curbing...

A Pendulum Experiment A pendulum of length L is suspended from the ceiling so it can swing freely; 9 denotes the angular displacement, in radians, from the vertical, as shown in Fig. 4.1. 12. The...

The 1.2-kg bob of a simple pendulum of length l = 600 mm is suspended from a 1.4-kg collar C. Knowing that the collar is acted upon by a periodic force P = Pm sin ft, where Pm = 0.5N and f = 3rad/s,...

The period T of a pendulum of length L is given by T = 2((L/g, where g is the acceleration of gravity. Show that dT/T = 1/2 [dL / L - dg/g], and use this result to estimate the maximum percentage...

A pendulum of length L has a bob of mass m attached to a light string, which is attached to a spring of force constant k. With the pendulum in the position shown in Figure, the spring is at its...

Please answer the following questions: Section 3 |Simple Harmonic Motion 25 Marks Q7. A homogeneous cylinder is connected to two identical springs as shown in the figure below: K K WWWWW m Figure 2...

Figure 8-34 shows a pendulum of length L = 1.25 m. Its bob (which effectively has all the mass) has speed v0 when the cord makes an angle 0 = 40.0o with the vertical. (a) What is the speed of the bob...

Take as much time needed to answer every single question. Just be sure to answer ead h question correctly and will write a wor iew about you afterwards! Do not rush and use the correct amount of...

A trolley of mass M is attached to ground via a spring of stiffness k and a damper of constant c as shown in Figure Q 3 . The trolley has a pendulum of length l with bob mass ( M ) attached. Assume...

1. [-/5 Points] DETAILS KATZPSEF1 5.P.041. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Two blocks are connected by a rope that passes over a massless and frictionless pulley as shown in the figure...

A Pendulum-and Spring System Mass m is on the end of a pendulum of length L and is also attached to a spring with constant k. Assume small oscillations of m so that the spring and the path of the...

Write a paper about The important of Human Resource Development (HRD) Specialist

Make the journal entries to record the purchase and use of direct materials and direct labour made by Dock Guard in E10-27A. In exercise Dock Guard, which uses a standard cost accounting system,...

A values statement is an organization's guiding principles, those things that the company believes to be important.

For the transfer function below, find the constraints on K 1 and K 2 such that the function will have only two j poles. K1s + K2 T(s) = s4 + K1s + s? + K2s + 1

Write a function that accepts temperature in degrees Fahrenheit (F) and computes the corresponding value in degrees Celsius (C). The relation between the two is Be sure to test your function. 5 ...

The current in a 25-mH inductor is given by the expressionsM i(t)=0 t 0 Find (a) the voltage across the inductor, (b) the expression for the energy stored in it.

The velocity of a particle which moves along the s-axis is given by v = 2 4t + 5t 3/2 , where t is in seconds and v is in meters per second. Evaluate the position s, velocity v, and acceleration a...

Show that every DCFG is an unambiguous CFG.

When will a court hold that there was no intention to create legal relations? How does such a fi nding differ from saying that there was an invitation to treat?

An electron (mass = 9.11 X 10-31 kg) leaves one end of a TV picture tube with zero initial speed and travels in a straight line to the accelerating grid, which is 1.80 cm away. It reaches the grid...

Superman throws a 2400-N boulder at an adversary. What horizontal force must Superman apply to the boulder to give it a horizontal acceleration of 12.0 m}S2?

A bowling ball weighs 71.2 N (16.0 Ib). The bowler applies a horizontal force of 160 N (36.0 lb) to the ball. What is the magnitude of the horizontal acceleration of the ball?

Question 1. Canada has had a Free Trade Agreement with the US and Mexico since 1994 so there are many years of quantifiable data to analyze its positive and negative effects. The new agreement, the...

You are considering the following two mutually exclusive projects. Both projects will be depreciated using straight-line depreciation to a zero book value over the life of the project. Neither...

4. Assuming a risk-free rate of 8 percent and a market return of 12 percent, would a wise investor acquire a security with a beta of 1.5 and a rate of return of 14 percent given the facts above? 5....