1. A harmonic oscillator consisting of a spring with unknown spring constant and

Question

1. A harmonic oscillator consisting of a spring with unknown spring constant and a mass of 0.28 kg has a period of 0.7 s. What is the spring constant (use units N/m)?

2. A simple harmonic oscillator consisting of a mass attached to a spring has a frequency of 2.74 Hz. If we now increase the mass by 24%, what is the new frequency of the oscillator?

3. An ideal massless spring is hanging vertically. When a 0.56-kg mass is attached to the spring, the spring stretches by 5.4 cm before reaching a new equilibrium. Then the mass is displaced by 2.7 cm from the new equlibrium. What is the frequency of the resulting oscillation?

Explanation / Answer

1)We know that,

w = sqrt (k/m)

2 pi/T = sqrt (k/m)

T = 2 pi sqrt (m/k)

T^2 = 4 pi^2 (m/k)

k = 4 pi^2 m/T^2

k = 4 x 3.14^2 x 0.28/0.7^2 = 22.54 N/m

Hence, k = 22.54 N/m

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