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
3.3 kgk = 170 N/m

A 3.3 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.3 kgk = 170 N/m
f = Hz
2.Easy
0.2 kgk = 200 N/m

A 0.2 kg mass on a spring with stiffness 200 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.2 kgk = 200 N/m
f = Hz
3.Medium
L = 2.7 m

A simple pendulum has a length of 2.7 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.7 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
0.9 kgk = 500 N/mA = 3 cm

A 0.9 kg mass on a spring with k = 500 N/m is pulled 3 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.9 kgk = 500 N/mA = 3 cm
E = J
6.Hard
0.8 kgk = 350 N/mA = 11 cm

A 0.8 kg mass on a spring with k = 350 N/m is pulled 11 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.8 kgk = 350 N/mA = 11 cm
E = J

Answer key

  1. 1. f = 1.142 Hz
  2. 2. f = 5.033 Hz
  3. 3. T = 3.296 s
  4. 4. L = 1.315 m
  5. 5. E = 0.225 J
  6. 6. E = 2.118 J

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