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 kgk21.5 cm

Hanging a 1 kg mass on a spring stretches it by 21.5 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 1 kgx = 21.5 cmg = 9.81 m/s²
T = s
2.Easy
3.2 kgk = 180 N/m

A 3.2 kg mass on a spring with stiffness 180 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.2 kgk = 180 N/m
f = Hz
3.Medium
t (s)x (cm)0.15 s

A 3.6 kg mass on a spring with k = 270 N/m is pulled 13 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.15 s (with sign).

m = 3.6 kgk = 270 N/mA = 13 cmt = 0.15 s
x = cm
4.Medium
L = 1.1 mT = 1.97 s

An astronaut on another planet finds that a simple pendulum 1.1 m long has a period of 1.97 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.1 mT = 1.97 s
g = m/s²
5.Hard
2 kgk = 100 N/m500 m/s

A 5 g bullet moving at 500 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 = 100 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 5 gv = 500 m/sM = 2 kgk = 100 N/m
A = cm
6.Hard
1 kgk = 30 N/mA = 9 cm

A 1 kg mass on a spring with k = 30 N/m is pulled 9 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1 kgk = 30 N/mA = 9 cm
amax = m/s²

Answer key

  1. 1. T = 0.9302 s
  2. 2. f = 1.194 Hz
  3. 3. x = 3.49 cm
  4. 4. g = 11.19 m/s²
  5. 5. A = 17.66 cm
  6. 6. amax = 2.7 m/s²

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