Physics - Simple Harmonic Motion (1 Viewer)

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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.
I got this to be x(t) = .25sin(8t)

b) What is the period T, of the subsequent oscillations?
I got the period to be .785 sec
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
If you have x(t), you can get all of the answers our of it. For instance, your w seems to be 8, which is the angular speed and equal to [tex]2 \pi / T[/tex].
For KE, you can simply get the 1st time derivative of x(t), and you have v(t), and calculate [tex]mv(4)^2/2[/tex].
As for the force, 1st time derivative of v(t) gives a(t), and all you need seems to be ma(1.2). Compare the signs of position and force at t=1.2, and you can conclude whether if they're pointing at the same direction or not. Finally, check out the sign of v(1.2) and happy end :)

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