Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A 2.1 kg mass on a spring with stiffness 360 N/m oscillates on a frictionless surface. Find the period T.

m = 2.1 kgk = 360 N/m

T = s

2.Easy

A 3 kg mass on a spring makes 50 complete oscillations in 19 s. Find the frequency f of the oscillation.

m = 3 kgN = 50t = 19 s

f = Hz

3.Medium

An astronaut on another planet finds that a simple pendulum 1.8 m long has a period of 2.83 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.8 mT = 2.83 s

g = m/s²

4.Medium

A 2.2 kg mass on a spring with k = 260 N/m is pulled 7 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.3 s (with sign).

m = 2.2 kgk = 260 N/mA = 7 cmt = 0.3 s

x = cm

5.Hard

An 8 g bullet moving at 250 m/s hits and stays in a 0.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 2000 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 250 m/sM = 0.5 kgk = 2000 N/m

A = cm

6.Hard

A 20 g bullet moving at 500 m/s hits and stays in a 3.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1100 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 500 m/sM = 3.5 kgk = 1100 N/m

A = cm

Answer key

1. T = 0.4799 s
2. f = 2.632 Hz
3. g = 8.873 m/s²
4. x = −6.95 cm
5. A = 6.275 cm
6. A = 16.07 cm

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