Question

A block of mass m is undergoing SHM on a horizontal, frictionless surface while attached to a light, horizontal spring. The spring has force constant k, and the amplitude of the SHM is A. The block has v = 0, and x = +A at t = 0. It first reaches x = 0 when t=T/4, where T is the period of the motion.

a) In terms of T, what is the time t when the block first reaches x=A/2?

b)The block has its maximum speed when t=T/4. What is the value of t when the speed of the block first reaches the value vmax/2?

c)(Hidden. will ask in comments)

Answer 1

a) The equation of motion is : x = A cos wt

when x=A/2, A/2 = A cos wt

cos wt = 1/2

wt = pi/3

2pi/T *t = pi/3

t = T/(2*3) = T/6 Answer

B] velocity v = dx/dt = -Aw *sin wt,

speed becomes half which means,

sin wt = 1/2

wt = pi/6

2pi/T t = pi/6

t = pi/6 *T/2pi

= T/12 answer