13.9 A spring with a spring constant of 450 N/m is stretched 15 cm from its equi

Question

13.9 A spring with a spring constant of 450 N/m is stretched 15 cm from its equilibrium position and released. a) If the mass attached to the spring is 2.5 kg, what is the frequency of the oscillation? b) What is the maximum kinetic energy of the mass? c) What is the maximum speed?

13.10 A 10 kg mass is attached to a spring with a spring constant of 1200 N/m. As the mass passes x = 12 cm, the speed is 4.25 m/s. a) What is the amplitude? b) What is the maximum speed? c) What is the energy of the system?

Explanation / Answer

a)We know that,

w = sqrt(k/m)

w = sqrt(450/2.5) = 13.42 rad/s

2 pi f = 13.42 => f = 13.42/2 x 3.14 = 2.14 Hz

Hence, f = 2.14 Hz

b)A = 15 cm = 0.15 m

v = w A = 13.42 x 0.15 = 2.01 m/s

KE = 1/2 m v^2

KE = 0.5 x 2.5 x 2.01^2 = 5.05 J

Hence, KE = 5.05 J

c)Max speed

v = w A = 13.42 x 0.15 = 2.01 m/s

Hence, v = 2.01 m/s

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