A ball whose mass is 1.8 kg is suspended from a spring whose stiffness is 4.5 N/

Question

A ball whose mass is 1.8 kg is suspended from a spring whose stiffness is 4.5 N/m. The ball oscillates up and down with an amplitude of 20 cm. (a) What is the angular frequency? radians/s (b) What is the frequency? hertz (cycles per second) (c) What is the period? T= d) Suppose you make it oscillate with an amplitude of 40 cm. Now what is the period? T. (e) Suppose this apparatus were taken to the Moon, where the strength of the gravitational field is only 1/6 of that on Earth. What would the period be on the Moon? (Consider carefully how the period depends on properties of the system look at the equation.)

Explanation / Answer

a) w = sqrt(k/m) = sqrt(4.5/1.8) = 1.58 rad/s

b) f = w/(2*pi) = 1.58/(2*3.142) = 0.252 cycles per sec

c) T = 1/f = 1/0.252 = 3.96 sec

d) T = 3.96 sec,Period does not depend on Amplitude

e) T = 2*pi*sqrt(m/k)

period T does not depend on the g

so T_moon = 3.96 sec

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