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
0.3 kgk = ?9.5 cm

Hanging a 0.3 kg mass on a spring stretches it by 9.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.3 kgx = 9.5 cmg = 9.81 m/s²
k = N/m
2.Easy
2.6 kgk

A 2.6 kg mass on a spring makes 15 complete oscillations in 28 s. Find the frequency f of the oscillation.

m = 2.6 kgN = 15t = 28 s
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.6 s? Use g = 9.81 m/s². Find L.

T = 2.6 sg = 9.81 m/s²
L = m
4.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
5.Hard
2.3 kgk = 130 N/mA = 2 cm

A 2.3 kg mass on a spring with k = 130 N/m is pulled 2 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.3 kgk = 130 N/mA = 2 cm
E = J
6.Hard
2 kgk = 400 N/m350 m/s

A 5 g bullet moving at 350 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 400 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 5 gv = 350 m/sM = 2 kgk = 400 N/m
A = cm

Answer key

  1. 1. k = 30.98 N/m
  2. 2. f = 0.5357 Hz
  3. 3. L = 1.68 m
  4. 4. T = 2.198 s
  5. 5. E = 0.026 J
  6. 6. A = 6.179 cm

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