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
2.7 kgk

A 2.7 kg mass on a spring makes 40 complete oscillations in 60 s. Find the frequency f of the oscillation.

m = 2.7 kgN = 40t = 60 s
f = Hz
2.Easy
4.1 kgk = ?

A 4.1 kg mass on a spring oscillates with a period of 0.4 s. Find the spring stiffness k.

m = 4.1 kgT = 0.4 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.9 s? Use g = 9.81 m/s². Find L.

T = 1.9 sg = 9.81 m/s²
L = m
4.Medium
L = 1.4 m

A simple pendulum has a length of 1.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.4 mg = 9.81 m/s²
T = s
5.Hard
3.4 kgk = 120 N/mA = 9 cm

A 3.4 kg mass on a spring with k = 120 N/m is pulled 9 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.4 kgk = 120 N/mA = 9 cm
E = J
6.Hard
3.5 kgk = 1100 N/m250 m/s

A 10 g bullet moving at 250 m/s hits and stays in a 3.5 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 = 10 gv = 250 m/sM = 3.5 kgk = 1100 N/m
A = cm

Answer key

  1. 1. f = 0.6667 Hz
  2. 2. k = 1012 N/m
  3. 3. L = 0.897 m
  4. 4. T = 2.374 s
  5. 5. E = 0.486 J
  6. 6. A = 4.023 cm

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