A body of mass is connected to a horizontal mass-less spring of force constant placed…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A body of mass m is connected to a horizontal mass-less spring of force constant k placed on a perfectly smooth surface. The body is displaced by a distance x=A from its equilibrium position and released from rest at t=0.
(i) Starting from the expression for the restoring force acting on the body, set up the differential equation governing its motion.
(ii) Solve the differential equation obtained in part (i) to obtain the general expression for the displacement x(t) of the body as a function of time.
(iii) Using the initial conditions given, write the particular form of x(t) for the motion described.