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A simple harmonic oscillator consists of a spring with a force constant of k = 59.5 N/m connected to a block with a mass of m = 1.05 kg. Assume that the surface supporting the block is flat and frictionless, and there is no air resistance. At time t = 0, the spring is stretched 16.5 cm from its natural length and the block is moving at a speed of 1.95 m/s in the -x direction, as shown below.
(a) Find x(t), the displacement of the block from equilibrium as a function of time. Hint: you'll need to find the constants ω (in rad/s), A (in cm), ?? (in radians) for the function: x(t) = Acos(ωt + φ).
(b) What is the velocity of the block (in m/s) at t = 2.00 s?
(c) What is the acceleration of the block (in m/s2) at t = 2.00 s?
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