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
0.5 kgk = ?

A 0.5 kg mass on a spring oscillates with a period of 2.4 s. Find the spring stiffness k.

m = 0.5 kgT = 2.4 s
k = N/m
2.Easy
1.4 kgk

A 1.4 kg mass on a spring makes 25 complete oscillations in 11 s. Find the frequency f of the oscillation.

m = 1.4 kgN = 25t = 11 s
f = Hz
3.Medium
L = 2.6 m

A simple pendulum has a length of 2.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.6 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.3 s? Use g = 9.81 m/s². Find L.

T = 2.3 sg = 9.81 m/s²
L = m
5.Hard
0.4 kgk = 370 N/mA = 7 cm

A 0.4 kg mass on a spring with k = 370 N/m is pulled 7 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.4 kgk = 370 N/mA = 7 cm
E = J
6.Hard
1.6 kgk = 160 N/mA = 5 cm

A 1.6 kg mass on a spring with k = 160 N/m is pulled 5 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.6 kgk = 160 N/mA = 5 cm
E = J

Answer key

  1. 1. k = 3.427 N/m
  2. 2. f = 2.273 Hz
  3. 3. T = 3.235 s
  4. 4. L = 1.315 m
  5. 5. E = 0.9065 J
  6. 6. E = 0.2 J

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