A mass is hanging motionless on a spring. The mass is pulled down 9 centimeters

Question

A mass is hanging motionless on a spring. The mass is pulled down 9 centimeters from that spot and released. What is the amplitude of the vibrational motion that follows? What distance does the mass travel during one full period of the motion? A spring has a length of 13 centimeters when unstretched, and a length of 42 centimeters when a 700 gram mass hangs motionless from it. A) Find the force constant of the spring. B) How much energy is stored in the spring with the mass hanging from it here?

Explanation / Answer

1. Amplitdue = 9 cm

distance travelled during one period = 4 (Amplitude )

= 36 cm

2. (A) Fnet = k deltax - mg = 0

k (0.42 -0.13) = 0.700 x 9.81

k = 23.7 N/m

(B) Stored energy = k (deltax)^2 / 2

= (23.7) (0.42 - 0.13)^2 / 2

= 1 J

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