Question

You attach a 2.50 kg mass to a horizontal spring that is fixed at one end. You pull the mass until the spring is stretched by 0.500 m and release it from rest. Assume the mass slides on a horizontal surface with negligible friction. The mass reaches a speed of zero again 0.300 s after release (for the first time after release). What is the maximum speed of the mass (in m/s)?

Answer 1

Given,

mass, m = 2.5 kg

Initial stretch, x = 0.5 m

Time taken to reach the speed of zero for the first time after release, t = 0.3 s

Since, the mass is kept on a frictionless horizontal surface, hence it will exhibit simple harmonic motion.

Thus,

Amplitude, A = 0.5 m

Time period is 2 times the time taken to reach the speed of zero for the first time

hence,

Time period, T = 0.6 s

Since frequency, f = 1/T

therefore, angular frequency, = 2f = 2/ T

                                                    = (2 * 3.14 ) / 0.6 = 10.47

Now, equation of SHM is

x(t) = A cos( t + )

Now, for = 0

x(t) = A cos( t )

v = dx(t) / dt = d/dt ( A cos( t ) )

                     = -A sin( t )

v(t) = -A sin( t )

Hence,

Max velocity = |-A| = 0.5 * 10.47

                      = 5.235 m/s