As the length of the pendulum increases, what happens to the total energy of the system?O decreasesO it decreases and increases as the pendulum oscillatesO remains the sameO increases

The total energy in pendulum system is mgL(1-cosθ) where m is mass of object , and L is length of…

Answered: As the length of the pendulum…

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter3: Oscillations

Section: Chapter Questions

Problem 3.45P: A grandfather clock has a pendulum length of 0.7 m and mass bob of 0.4 kg. A mass of 2 kg falls 0.8...

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A simple pendulum as shown in Fig. 4.24 oscillates back and forth. Use the letter designations in the figure to identify the pendulums position(s) for the following conditions. (There may be more than one answer. Consider the pendulum to be ideal with no energy losses.) (a) Position(s) of instantaneous rest ___ (b) Position(s) of maximum velocity ___ (c) Position(s) of maximum Ek ___ (d) Position(s) of maximum Ep ___ (e) Position(s) of minimum Ek ___ (f) Position(s) of minimum Ep ___ (g) Position(s) after which Ek increases ___ (h) Position(s) after which Ep increases ___ (i) Position(s) after which Ek decreases ___ (j) Position(s) after which Ep decreases ___ Figure 4.24 The Simple Pendulum and Energy
Give an example of a damped harmonic oscillator. (They are more common than undamped or simple harmonic oscillators.)
If the speed of the observer is increased by 5.0%, what is the period of the pendulum when measured by this observer?
If a simple pendulum oscillates with small amplitude and its length is doubled, what happens to the frequency of its motion? (a) It doubles. (b) It becomes 2 times as large. (c) It becomes half as large. (d) It becomes 1/2 times as large. (e) It remains the same.
If the amplitude of a damped oscillator decreases to 1/e of its initial value after n periods, show that the frequency of the oscillator must be approximately [1 − (8π2n2)−1] times the frequency of the corresponding undamped oscillator.
Check Your Understanding An engineer builds two simple pendulums. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10 kg. Pendulum 2 has a bob with a mass of 100 kg. Describe how the motion of the pendulums will differ if the bobs are both displaced by 12°.
A pendulum clock works by measuring the period of a pendulum. In the springtime the clock runs with perfect time, but in the summer and winter the length of the pendulum changes. When most materials are heated, they expand. Does the clock run too fast or too slow in the summer? What about the winter?
Two parakeets sit on a swing with their combined CMs 10.0 cm below the pivot. At what frequency do they swing?
A grandfather clock has a pendulum length of 0.7 m and mass bob of 0.4 kg. A mass of 2 kg falls 0.8 m in seven days to keep the amplitude (from equilibrium) of the pendulum oscillation steady at 0.03 rad. What is the Q of the system?
Show that the time rate of change of mechanical energy for a damped, undriven oscillator is given by dE/dt = bv2 and hence is always negative. To do so, differentiate the expression for the mechanical energy of an oscillator, E=12mv2+12kx2, and use Equation 15.51.
A 50.0-g object connected to a spring with a force constant of 35.0 N/m oscillates with an amplitude of 4.00 cm on a frictionless, horizontal surface. Find (a) the total energy of the system and (b) the speed of the object when its position is 1.00 cm. Find (c) the kinetic energy and (d) the potential energy when its position is 3.00 cm.
A pendulum dork depends on the period of a pendulum to keep correct time. Suppose a pendulum dock is keeping correct time and then Dennis the Menace slides the bob of the pendulum downward on the oscillating rod. Does the clock run (a) slow, (b) fast, or (c) correctly?

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As the length of the pendulum increases, what happens to the total energy of the system? O decreases O it decreases and increases as the pendulum oscillates remains the same O increases