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
1.9 kgk = ?

A 1.9 kg mass on a spring oscillates with a period of 1.45 s. Find the spring stiffness k.

m = 1.9 kgT = 1.45 s
k = N/m
2.Easy
4.2 kgk = 150 N/m

A 4.2 kg mass on a spring with stiffness 150 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.2 kgk = 150 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 0.8 s? Use g = 9.81 m/s². Find L.

T = 0.8 sg = 9.81 m/s²
L = m
4.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
5.Hard
0.6 kgk = 270 N/mA = 13 cm

A 0.6 kg mass on a spring with k = 270 N/m is pulled 13 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.6 kgk = 270 N/mA = 13 cm
amax = m/s²
6.Hard
2.8 kgk = 270 N/mA = 13 cm

A 2.8 kg mass on a spring with k = 270 N/m is pulled 13 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.8 kgk = 270 N/mA = 13 cm
E = J

Answer key

  1. 1. k = 35.68 N/m
  2. 2. f = 0.9511 Hz
  3. 3. L = 0.159 m
  4. 4. L = 1.68 m
  5. 5. amax = 58.5 m/s²
  6. 6. E = 2.282 J

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