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**1. Homework Statement**

Consider the simple harmonic motion of a block attached to a spring on a horizontal surface (assume no damping to begin with). At t = 0, the potential energy in the spring is 25% of the maximum potential energy during this motion. Moreover, the kinetic energy of the block is decreasing with time at t = 0 and, at t = 2.0 s, the kinetic energy becomes zero for the 1st time (after t = 0).

(i) What is the frequency of this motion?

(ii) What is the spring constant if the mass of the block is 2 kg?

(iii) If the total energy of the system is 10 −2 J, then what is the amplitude of the motion?

(iv) Next, a drag force is added with a damping constant of 0.2 kg/s. At what time will the

energy in the motion reduce to 25% of the energy at t = 0?

**2. Homework Equations**

F = 1/ T

x(t) = Acos(2*pi*t/T)

omega = 2 * pie * frequency

Xmax(t) = Ae^(-bt/2m) **FOR PART 4

**3. The Attempt at a Solution**

I drew up the image of the simple harmonic motion and i figured that if i find the time it takes to make one oscillation, i could then find the frequency (F =1/T). However, It feels like a guessing game for the time. According to the drawing, it takes about 3 seconds to make a full oscillation; does that sound right? That would mean the frequency would be .33 hertz.

For part ii, the spring constant is : k = omega^2*mass. Omega is our unknown and I would assume as 2 * pie * frequency. But im nervous my frequency is wrong.

For part iii, you can use the equation x(t) = Acos(omega + phase constant). Can I assume the phase constant to be zero? If so, we can use the above formula to solve for A.

Part 4, we use the above formula and were given the damping constant but I'm confused on the topic of damping oscillations and not sure where to go with the formula.

All advise, hints, tips, and help will be greatly appreciated. If I can rep people, I will do that as well for help.

-UMDstudent