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 kgk = 300 N/m

A 2 kg mass on a spring with stiffness 300 N/m oscillates on a frictionless surface. Find the period T.

m = 2 kgk = 300 N/m
T = s
2.Easy
0.3 kgk = ?

A 0.3 kg mass on a spring oscillates with a period of 1.25 s. Find the spring stiffness k.

m = 0.3 kgT = 1.25 s
k = N/m
3.Medium
L = 1.8 mT = 2.83 s

An astronaut on another planet finds that a simple pendulum 1.8 m long has a period of 2.83 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.8 mT = 2.83 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.4 s? Use g = 9.81 m/s². Find L.

T = 1.4 sg = 9.81 m/s²
L = m
5.Hard
2.5 kgk = 120 N/mA = 18 cm

A 2.5 kg mass on a spring with k = 120 N/m is pulled 18 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.5 kgk = 120 N/mA = 18 cm
E = J
6.Hard
mk = 310 N/mA = 10 cmx = 3 cm

A mass on a spring with k = 310 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find the energy U stored in the spring when the mass is 3 cm from equilibrium.

k = 310 N/mA = 10 cmx = 3 cm
U = J

Answer key

  1. 1. T = 0.513 s
  2. 2. k = 7.58 N/m
  3. 3. g = 8.873 m/s²
  4. 4. L = 0.487 m
  5. 5. E = 1.944 J
  6. 6. U = 0.1395 J

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