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
0.2 kgk5.5 cm

Hanging a 0.2 kg mass on a spring stretches it by 5.5 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 0.2 kgx = 5.5 cmg = 9.81 m/s²
T = s
2.Easy
4.6 kgk = 20 N/m

A 4.6 kg mass on a spring with stiffness 20 N/m oscillates on a frictionless surface. Find the period T.

m = 4.6 kgk = 20 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.2 s? Use g = 9.81 m/s². Find L.

T = 1.2 sg = 9.81 m/s²
L = m
4.Medium
L = 0.9 mT = 2 s

An astronaut on another planet finds that a simple pendulum 0.9 m long has a period of 2 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.9 mT = 2 s
g = m/s²
5.Hard
1 kgk = 100 N/m200 m/s

A 20 g bullet moving at 200 m/s hits and stays in a 1 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 100 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 200 m/sM = 1 kgk = 100 N/m
A = cm
6.Hard
1.2 kgk = 160 N/mA = 14 cm

A 1.2 kg mass on a spring with k = 160 N/m is pulled 14 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.2 kgk = 160 N/mA = 14 cm
E = J

Answer key

  1. 1. T = 0.4705 s
  2. 2. T = 3.013 s
  3. 3. L = 0.3578 m
  4. 4. g = 8.883 m/s²
  5. 5. A = 39.61 cm
  6. 6. E = 1.568 J

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