Question

0.50 Time (s) 4.0 6.0 2.0 -0.50 Displacement (m)

Use the conservation of energy to find the speed of the mass (2.8kg) when the spring has its normal length x=0.

Answer 1

From the graph Time period T = 4 sec T = 2 pi/w 4 = 2 pi/w w = 2 pi/4 = pi/2 rads Amplitude = 0.5 m At normal length, (x = 0) potential energy = 0 By using energy conservation: - P.E + K.E = total energy(mechanical energy) 0 + 1/2 mv^2 = 1/2 kA^2 1/2 mv^2 = 1/2 m w^2 A^2 [k = mw] v^2 = w^2 A^2 v = A w = 0.5 times pi/2 = 5/10 times pi/2 v = pi/4 m/s