A particle with mass 1.01 kg oscillates horizontally at the end of a horizontal

Question

A particle with mass 1.01 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.993 m and a duration of 129 s for 61 cycles of oscillation. Find the frequency, f, the speed at the equilibrium position, vmax, the spring constant. K the potential energy at an endpoint. Umax,. the potential energy when the part d o is located 65 9 % of the amplitude away from the equilibrium position. U,. and the kinetic energy, K, and the speed, v, at the same position.

Explanation / Answer

129 s>61 cycles
so 1 cycle has time 129/61=2.11s
T=2.11s=1/f

f=0.474 Hz

=(k/m)

=2f=2.98 rad/s

k=8.96 N/m

vmax=A==2.96 m/s

Umax=1/2kA2=4.42J

A1=.659A

U=1.92J

K=Umax-U=2.5 J

v=(2K/m)=2.226 m/s

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