A simple harmonic oscillator consists of a block with mass 3.00 kg attached to a

Question

A simple harmonic oscillator consists of a block with mass 3.00 kg attached to a spring with spring constant k = 150 N/m. At time t = 0.50 s, the position and velocity of the block are x = 0.250 m and v = 3.5 m/s. The oscillation is horizontal (gravity may be ignored) and takes place on a frictionless surface. a. What is the amplitude of the oscillation? b. What was the position of the block at t = 0? c. What was the velocity of the block at t = 0? d. What is the phase lag (Express your answer in radians).

Explanation / Answer

m = 3.00 kg, k = 150 N/m, so = (k/m) = 50 rad/s
at t = 0.50 s, x = 0.250 m, v = 3.5 m/s,
a) find A
A = (x2 + v2/2) = 0.555 m

b) find x at t = 0

let x = Asin(t + ), so v = Acos(t + )

at t = 0.50 s,

0.250 = 0.555sin(50 * 0.50 + ), sin(3.54 + ) = 0.450

and v > 0, or cos(t + ) > 0, so 3.54 + = 0.47, = -3.07 rad

at t = 0, x = Asin = 0.555sin(-3.07) = -0.0397 m

c) v = Acos = -3.91 m/s

d) || = 3.07 rad

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