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
1.3 kgk = 210 N/m

A 1.3 kg mass on a spring with stiffness 210 N/m oscillates on a frictionless surface. Find the period T.

m = 1.3 kgk = 210 N/m
T = s
2.Easy
3 kgk = ?8.5 cm

Hanging a 3 kg mass on a spring stretches it by 8.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 3 kgx = 8.5 cmg = 9.81 m/s²
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.5 s? Use g = 9.81 m/s². Find L.

T = 2.5 sg = 9.81 m/s²
L = m
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
mk = 20 N/mA = 12 cmx = 8 cm

A mass on a spring with k = 20 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find the energy U stored in the spring when the mass is 8 cm from equilibrium.

k = 20 N/mA = 12 cmx = 8 cm
U = J
6.Hard
3 kgk = 1100 N/m250 m/s

A 20 g bullet moving at 250 m/s hits and stays in a 3 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1100 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 250 m/sM = 3 kgk = 1100 N/m
A = cm

Answer key

  1. 1. T = 0.4944 s
  2. 2. k = 346.2 N/m
  3. 3. L = 1.553 m
  4. 4. g = 11.19 m/s²
  5. 5. U = 0.064 J
  6. 6. A = 8.675 cm

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