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
1.8 kgk = 100 N/m

A 1.8 kg mass on a spring with stiffness 100 N/m oscillates on a frictionless surface. Find the period T.

m = 1.8 kgk = 100 N/m
T = s
2.Easy
1 kgk = 110 N/m

A 1 kg mass on a spring with stiffness 110 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1 kgk = 110 N/m
f = Hz
3.Medium
L = 1.2 m

A simple pendulum has a length of 1.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.2 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
5.Hard
2.2 kgk = 170 N/mA = 2 cm

A 2.2 kg mass on a spring with k = 170 N/m is pulled 2 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.2 kgk = 170 N/mA = 2 cm
E = J
6.Hard
3.1 kgk = 160 N/mA = 18 cm

A 3.1 kg mass on a spring with k = 160 N/m is pulled 18 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.1 kgk = 160 N/mA = 18 cm
E = J

Answer key

  1. 1. T = 0.843 s
  2. 2. f = 1.669 Hz
  3. 3. T = 2.198 s
  4. 4. L = 0.8051 m
  5. 5. E = 0.034 J
  6. 6. E = 2.592 J

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