Question

Consider a simple pendulum with a bob of mass 4.0 kg and a string of length 45 cm.

Part A: Which of the following is true for small angular displacement?
a. The net torque is proportional to the negative of the angle displaced from the equilibrium
b. The period is inversely proportional to the amplitude
c. The kinetic energy is always equal to the potential energy
d. The minimum velocity is achieved when the bob is at equilibrium

Part B: If the bob is released from rest at a starting angle of 9 degrees, what is the max speed of the bob in cm/s?

Answer 1

(A) it's answer is option number (a)

Torque is proportional to the negative of angle displaced from the equilibrium.

Torque = - mg L sin

For small angle sin =

Thus , torque = - mg L

( B) For small angle

V_{​​​​​​ Max} = √( gl ²) = √ ( 9.8× 0.45× 0.157× 0.157)

= 32.97 cm/s

Here 0.157 rad = 9°