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
1.1 kgk = 120 N/m

A 1.1 kg mass on a spring with stiffness 120 N/m oscillates on a frictionless surface. Find the period T.

m = 1.1 kgk = 120 N/m
T = s
2.Easy
2.6 kgk = ?

A 2.6 kg mass on a spring makes 30 complete oscillations in 49 s. Find the spring stiffness k.

m = 2.6 kgN = 30t = 49 s
k = N/m
3.Medium
L = 1.8 mT = 6.62 s

An astronaut on another planet finds that a simple pendulum 1.8 m long has a period of 6.62 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.8 mT = 6.62 s
g = m/s²
4.Medium
L = 1.9 m

A simple pendulum has a length of 1.9 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.9 mg = 9.81 m/s²
T = s
5.Hard
1.5 kgk = 400 N/m500 m/s

A 20 g bullet moving at 500 m/s hits and stays in a 1.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 400 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 500 m/sM = 1.5 kgk = 400 N/m
A = cm
6.Hard
2.6 kgk = 190 N/mA = 17 cm

A 2.6 kg mass on a spring with k = 190 N/m is pulled 17 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.6 kgk = 190 N/mA = 17 cm
vmax = m/s

Answer key

  1. 1. T = 0.6016 s
  2. 2. k = 38.48 N/m
  3. 3. g = 1.621 m/s²
  4. 4. T = 2.765 s
  5. 5. A = 40.56 cm
  6. 6. vmax = 1.453 m/s

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