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
0.8 kgk

A 0.8 kg mass on a spring makes 25 complete oscillations in 33 s. Find the frequency f of the oscillation.

m = 0.8 kgN = 25t = 33 s
f = Hz
2.Easy
3.2 kgk

A 3.2 kg mass on a spring makes 50 complete oscillations in 31 s. Find the frequency f of the oscillation.

m = 3.2 kgN = 50t = 31 s
f = Hz
3.Medium
L = 2.5 m

A simple pendulum has a length of 2.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.5 mg = 9.81 m/s²
T = s
4.Medium
L = 1.8 mT = 2.52 s

An astronaut on another planet finds that a simple pendulum 1.8 m long has a period of 2.52 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.8 mT = 2.52 s
g = m/s²
5.Hard
0.5 kgk = 700 N/m350 m/s

A 12 g bullet moving at 350 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 = 700 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 350 m/sM = 0.5 kgk = 700 N/m
A = cm
6.Hard
2 kgk = 1800 N/m350 m/s

A 10 g bullet moving at 350 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1800 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 10 gv = 350 m/sM = 2 kgk = 1800 N/m
A = cm

Answer key

  1. 1. f = 0.7576 Hz
  2. 2. f = 1.613 Hz
  3. 3. T = 3.172 s
  4. 4. g = 11.19 m/s²
  5. 5. A = 22.19 cm
  6. 6. A = 5.819 cm

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