A mass m=1 kg can slide without friction on a plane, and is attached to a spring

Question

A mass m=1 kg can slide without friction on a plane, and is attached to a spring of elastic constant k= 1N/m. The x axis is oriented along the direction of stretch. The origin of the reference frame coincides with the equilibrium position of the mass. At time t=0, the mass is at the equilibrium position, and is truck with velocity of 10 cm/s to the left, so the spring is compressed. Determine the position and velocity of the mass after 5 seconds. Specify whether it is moving left or right at t=5 s.

Explanation / Answer

mass m = 1 kg spring constant   k = 1 N / m initial velocity of the mass u  = 10 cm / s = 0.1 m / s            restoring force on the mass                 F = - k x               m a =   kx               acceleration of the  mass    a = - x   where   x = displacement of mass                   final velocity of the mass                   v = u + at                      =   u - 5 x                      = 0.1 - 5 x             position of mass                 s = v^2 - u^2 / 2 a       here x value is not given        plug the value of x and get the answers

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