A harmonic oscillator consisting of an ideal spring attached to a mass has a per

Question

1. A harmonic oscillator consisting of an ideal spring attached to a mass has a period of 1.4 s. The oscillator is displaced from the equilibrium position by 2.7 cm and then released. What is the speed of the mass when it has returned half the distance to the equilibrium position?

A harmonic oscillator consisting of an ideal spring attached to a mass has a period of 1.4 s. The oscillator is displaced from the equilibrium position by 2.7 cm and then released. What is the speed of the mass when it has returned half the distance to the equilibrium position? A harmonic oscillator consisting of an ideal spring attached to a mass has a period of 1.4 s. The oscillator is displaced from the equilibrium position by 2.7 cm and then released. What is the speed of the mass when it has returned half the distance to the equilibrium position?

Explanation / Answer

T=2pi/w

w=2*pi/1.4

==> w=sqrt(k/m) = 2*pi/1.4 = 4.487

1/2*KA^2= 1/2K(A/2)^2 +1/2mv^2

==> v^2=(K/m)*(3A^2/4)

==> v=sqrt(K/m)*sqrt(3/4)*A

==> v=4.487*sqrt(3/4)*0.027= 0.1049 m/s = 10.49 cm/s

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