Question

A mass on a spring undergoes simple harmonic motion. At t = 0 its displacement is 1m and its velocity is 1m/s towards the equilibrium position. What single piece of information allows you to determine frequency and amplitude?

A. mass

B. spring constant (k)

C. kinetic energy at t = 0

D. acceleration at t = 0

E. force at t = 0

Answer 1

given :

displacement = x = 1 m

instantaneous velocity = v = 1 m/s

formula for displacement is given as

x =

formula for frquency

hence to find out frequency and amplitude we need value of .

option A) mass - not sufficient

as both the formulaes do not require mass information

option B) spring constant = k = - not sufficient

as we also neeed value of mass to find out

option c) kinetic energy at t = 0 - K.E. = - not sufficient

it also requires value of mass to find .

option D) acceleration = - - sufficient

using acceleration we can find and this value will be needed to find amplitude and frequency.

option E) force at t = 0 - not sufficient

F = - kx

using force value we can find k and to find again we require value of mass which is not provided.