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
2.2 kgk = ?9.5 cm

Hanging a 2.2 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 = 2.2 kgx = 9.5 cmg = 9.81 m/s²
k = N/m
2.Easy
3.4 kgk = 10 N/m

A 3.4 kg mass on a spring with stiffness 10 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.4 kgk = 10 N/m
f = Hz
3.Medium
L = 2.5 m

A simple pendulum has a length of 2.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.5 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.9 s? Use g = 9.81 m/s². Find L.

T = 2.9 sg = 9.81 m/s²
L = m
5.Hard
1 kgk = 80 N/mA = 18 cm

A 1 kg mass on a spring with k = 80 N/m is pulled 18 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1 kgk = 80 N/mA = 18 cm
amax = m/s²
6.Hard
4 kgk = 500 N/mA = 6 cm

A 4 kg mass on a spring with k = 500 N/m is pulled 6 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 4 kgk = 500 N/mA = 6 cm
E = J

Answer key

  1. 1. k = 227.2 N/m
  2. 2. f = 0.2729 Hz
  3. 3. T = 3.172 s
  4. 4. L = 2.09 m
  5. 5. amax = 14.4 m/s²
  6. 6. E = 0.9 J

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