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
2.3 kgk = ?

A 2.3 kg mass on a spring oscillates with a period of 1.25 s. Find the spring stiffness k.

m = 2.3 kgT = 1.25 s
k = N/m
2.Easy
2.8 kgk = ?

A 2.8 kg mass on a spring oscillates with a period of 2.3 s. Find the spring stiffness k.

m = 2.8 kgT = 2.3 s
k = N/m
3.Medium
L = 1.9 mT = 6.8 s

An astronaut on another planet finds that a simple pendulum 1.9 m long has a period of 6.8 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.9 mT = 6.8 s
g = m/s²
4.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
5.Hard
0.6 kgk = 210 N/mA = 9 cm

A 0.6 kg mass on a spring with k = 210 N/m is pulled 9 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.6 kgk = 210 N/mA = 9 cm
E = J
6.Hard
1.5 kgk = 400 N/m200 m/s

A 5 g bullet moving at 200 m/s hits and stays in a 1.5 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 = 200 m/sM = 1.5 kgk = 400 N/m
A = cm

Answer key

  1. 1. k = 58.11 N/m
  2. 2. k = 20.9 N/m
  3. 3. g = 1.622 m/s²
  4. 4. L = 0.897 m
  5. 5. E = 0.8505 J
  6. 6. A = 4.076 cm

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