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
3.8 kgk = 110 N/m

A 3.8 kg mass on a spring with stiffness 110 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.8 kgk = 110 N/m
f = Hz
2.Easy
0.7 kgk = ?

A 0.7 kg mass on a spring oscillates with a period of 2.5 s. Find the spring stiffness k.

m = 0.7 kgT = 2.5 s
k = N/m
3.Medium
L = 2.2 m

A simple pendulum has a length of 2.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.2 mg = 9.81 m/s²
T = s
4.Medium
L = 0.5 mT = 3.49 s

An astronaut on another planet finds that a simple pendulum 0.5 m long has a period of 3.49 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.5 mT = 3.49 s
g = m/s²
5.Hard
mk = 110 N/mA = 8 cmx = 3 cm

A mass on a spring with k = 110 N/m oscillates on a frictionless surface with an amplitude of 8 cm. Find its kinetic energy K when it is 3 cm from equilibrium.

k = 110 N/mA = 8 cmx = 3 cm
K = J
6.Hard
mk = 330 N/mA = 5 cmx = 1 cm

A mass on a spring with k = 330 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find its kinetic energy K when it is 1 cm from equilibrium.

k = 330 N/mA = 5 cmx = 1 cm
K = J

Answer key

  1. 1. f = 0.8563 Hz
  2. 2. k = 4.422 N/m
  3. 3. T = 2.975 s
  4. 4. g = 1.621 m/s²
  5. 5. K = 0.3025 J
  6. 6. K = 0.396 J

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