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
1.6 kgk = 350 N/m

A 1.6 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.6 kgk = 350 N/m
f = Hz
2.Easy
2.1 kgk = 280 N/m

A 2.1 kg mass on a spring with stiffness 280 N/m oscillates on a frictionless surface. Find the period T.

m = 2.1 kgk = 280 N/m
T = s
3.Medium
L = 1.3 m

A simple pendulum has a length of 1.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.3 mg = 9.81 m/s²
T = s
4.Medium
L = 1.1 mT = 1.32 s

An astronaut on another planet finds that a simple pendulum 1.1 m long has a period of 1.32 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.1 mT = 1.32 s
g = m/s²
5.Hard
mk = 350 N/mA = 9 cmx = 6 cm

A mass on a spring with k = 350 N/m oscillates on a frictionless surface with an amplitude of 9 cm. Find its kinetic energy K when it is 6 cm from equilibrium.

k = 350 N/mA = 9 cmx = 6 cm
K = J
6.Hard
0.5 kgk = 180 N/mA = 18 cm

A 0.5 kg mass on a spring with k = 180 N/m is pulled 18 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.5 kgk = 180 N/mA = 18 cm
E = J

Answer key

  1. 1. f = 2.354 Hz
  2. 2. T = 0.5441 s
  3. 3. T = 2.287 s
  4. 4. g = 24.92 m/s²
  5. 5. K = 0.7875 J
  6. 6. E = 2.916 J

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