Q33 of 40 Page 103

A mass of 2 kg is attached to the spring of spring constant 50 Nm-1. The block is pulled to a distance of 5cm from its equilibrium position at x = 0 on a horizontal frictionless surface from rest at t = 0. Write the expression for its displacement at any time t.

For simple harmonic motion, the displacement equation is given as follows,


----(1)


where x = displacement


w= angular velocity


A = amplitude


We will be finding each parameter from the given data and then substitute in the above equation


Given:


mass m


spring constant


amplitude ------(2)


time period for S.H.M.



Putting the values, we get,



Now we need angular velocity


Which is written as,


∴ ----(3)


Putting (2) and (3) in (1) we get,



the expression for its displacement at any time t is given as




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