Simple pendulum and dissipation of energy — practice questions

Question 1 · difficulty L1 · recall

For small oscillations, the time period of a simple pendulum is approximately

• A. T=2πsqrt(g/L)
• B. T=L/g
• C. T=2πsqrt(L/g)
• D. T=2πL/g

Question 2 · difficulty L1 · understanding

The period of a simple pendulum is approximately independent of

• A. pendulum length
• B. local g
• C. large amplitude outside the small-angle limit
• D. bob mass

Question 3 · difficulty L2 · understanding

If pendulum length is quadrupled, its small-angle period becomes

• A. twice
• B. four times
• C. half
• D. unchanged

Question 4 · difficulty L2 · application

To reduce timing reaction error in a pendulum experiment, one should time

• A. only a fraction of one oscillation
• B. many oscillations and divide by their number
• C. one oscillation repeatedly without averaging
• D. the bob mass

Question 5 · difficulty L3 · application

Damping causes pendulum amplitude to

• A. increase indefinitely
• B. remain exactly constant in air
• C. decrease with time
• D. reverse sign permanently after each cycle

Question 6 · difficulty L3 · application

In a damped pendulum, lost mechanical energy is mainly converted into

• A. extra gravitational potential that accumulates forever
• B. mass
• C. electric charge
• D. thermal energy and sound in the surroundings

Question 7 · difficulty L4 · analysis

A graph of amplitude versus time for a lightly damped pendulum is expected to show

• A. a gradually decaying envelope
• B. constant amplitude forever
• C. linear growth without bound
• D. instantaneous zero after one cycle

Question 8 · difficulty L4 · analysis

If measured period is used to find g, the relation is

• A. g=T²/(4π²L)
• B. g=4π²L/T²
• C. g=2πL/T
• D. g=LT²

Question 9 · difficulty L5 · analysis

A student measures time for 20 oscillations as 40.0 s. The estimated period is

• A. 20.0 s
• B. 0.50 s
• C. 2.00 s
• D. 800 s

Question 10 · difficulty L5 · analysis

Why should the pendulum amplitude be kept small in the standard g experiment?

• A. To make bob mass zero
• B. To eliminate gravity
• C. To force period to depend strongly on amplitude
• D. So the small-angle approximation underlying T=2πsqrt(L/g) remains valid