At what time t1 does the block come back to its original equilibrium position (x=0) for the first time? Express your answer in terms of some or all of the variables: A, k, and m.

t_1 = 0.5*pi*sqrt (m / k)

Explanation:

Given:

- The block of mass m undergoes simple harmonic motion. With the displacement of x from mean position is given by:

x (t) = A*cos (w*t)

Find:

- At what time t1 does the block come back to its original equilibrium position (x=0) for the first time?

Solution:

- The first time the block moves from maximum position to its mean position constitutes of 1/4 th of one complete cycle. So, the required time t_1 is:

t_1 = 0.25*T

- Where, T : Time period of SHM.

- The time period for SHM is given by:

T = 2*pi*sqrt (m / k)

Hence,

t_1 = 0.25 * 2 * pi * sqrt (m / k)

t_1 = 0.5*pi * sqrt (m / k)