Homework Answers
a) Apply conservation of energy
(1/2)*(m1 + m2)*v^2 = (1/2)*k*A^2
v^2 = k*A^2/(m1 + m2)
v = sqrt(k/(m1 + m2) )*A
= sqrt(100/(8.1 + 7) )*0.16
= 0.412 m/s <<<<<<<<<<<------------------Answer
b) let A' is the new amplitude.
now Apply conservation of energy
(1/2)*k*A'^2 = (1/2)*m1*v^2
A'^2 = m1*v^2/k
A' = sqrt(m1/k)*v
= sqrt(8.1/100)*0.412
= 0.117 m
Time period of the oscillations, T = 2*pi*sqrt(m1/k)
= 2*pi*sqrt(8.1/100)
= 1.79 s
time taken to move from mean position to maximum extension, t = T/4
= 1.79/4
so, D = v*t - A
= 0.412*(1.79/4) - 0.117
= 0.0674 m <<<<<<<<<<<------------------Answer
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