Physics: Calculate x(t), T & Kinetic Energy, Find Force & Direction of Block

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The discussion focuses on a physics problem involving a block of mass 0.5 kg colliding with a massless pan attached to a spring with a spring constant of 32 N/m. The function for displacement x(t) is derived using harmonic motion equations. The period T of the oscillations is calculated, and the kinetic energy of the block is determined 4.0 seconds post-collision. Additionally, the force exerted by the spring on the block at t=1.2 seconds is analyzed, along with the direction of the block's movement.

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A block of mass 0.5kg moving on a horizontal frictionless surface at 2.0 m/s collides with and sticks to a massless pan attached to the end of a horizontal ideal spring whose spring constan is 32 N/m.
a) Determine the function for x(t), the displacement from equilibrium position as a function of time.
b) What is the period T, of the subsequent oscillations?
c) What is the kinetic energy of the mass 4.0 sec after it collides with the spring?
d) What force is exerted by the spring on the block at t=1.2 sec? Which way is the block moving? Explain
 
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