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
1.4 kgk = 230 N/m

A 1.4 kg mass on a spring with stiffness 230 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.4 kgk = 230 N/m
f = Hz
2.Easy
2.6 kgk = 370 N/m

A 2.6 kg mass on a spring with stiffness 370 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.6 kgk = 370 N/m
f = Hz
3.Medium
L = 1.2 mT = 3.57 s

An astronaut on another planet finds that a simple pendulum 1.2 m long has a period of 3.57 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.2 mT = 3.57 s
g = m/s²
4.Medium
L = 1 mT = 1.26 s

An astronaut on another planet finds that a simple pendulum 1 m long has a period of 1.26 s for small swings. Find the gravitational acceleration g on that planet.

L = 1 mT = 1.26 s
g = m/s²
5.Hard
mk = 380 N/mA = 6 cmx = 4 cm

A mass on a spring with k = 380 N/m oscillates on a frictionless surface with an amplitude of 6 cm. Find its kinetic energy K when it is 4 cm from equilibrium.

k = 380 N/mA = 6 cmx = 4 cm
K = J
6.Hard
mk = 230 N/mA = 4 cmx = 1 cm

A mass on a spring with k = 230 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find the energy U stored in the spring when the mass is 1 cm from equilibrium.

k = 230 N/mA = 4 cmx = 1 cm
U = J

Answer key

  1. 1. f = 2.04 Hz
  2. 2. f = 1.899 Hz
  3. 3. g = 3.717 m/s²
  4. 4. g = 24.87 m/s²
  5. 5. K = 0.38 J
  6. 6. U = 0.0115 J

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