A simple harmonic oscillator consists of a block of mass 500

A simple harmonic oscillator consists of a block of mass 5.00 kg attached to a spring of spring constant 110 N/m. When t = 1.10 s, the position and velocity of the block are x = 0.124 m and v = 2.950 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?

Solution

m = mass = 5.00 kg

k = spring constant = 110 N/m

a)

using conservation of energy

maximum spring energy = spring energy at x = 0.124   + KE

(0.5) k A² = (0.5) k x² + (0.5) m v²

(110) A² = (110) (0.124)² + (2.50) (2.950)²

A = 0.4616 m

(b)

x = A*sin(w*t + phi)

at t=o

x = 0.4616*sin(0-0.53)

x = -0.252 m

(c)

w = sqrt (110/5)

at t = 0

v = w * A*cos(w*t + phi)

v = 4.69*0.4616 *cos(0-0.53)

v = 2.05 m/s