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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
2.4 kgk = ?5.5 cm

Hanging a 2.4 kg mass on a spring stretches it by 5.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.4 kgx = 5.5 cmg = 9.81 m/s²
k = N/m
2.Easy
2.6 kgk = ?

A 2.6 kg mass on a spring makes 25 complete oscillations in 37 s. Find the spring stiffness k.

m = 2.6 kgN = 25t = 37 s
k = N/m
3.Medium
t (s)x (cm)1 s

A 3.7 kg mass on a spring with k = 360 N/m is pulled 14 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1 s (with sign).

m = 3.7 kgk = 360 N/mA = 14 cmt = 1 s
x = cm
4.Medium
L = 1.6 m

A simple pendulum has a length of 1.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.6 mg = 9.81 m/s²
T = s
5.Hard
mk = 480 N/mA = 19 cmx = 17 cm

A mass on a spring with k = 480 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find the energy U stored in the spring when the mass is 17 cm from equilibrium.

k = 480 N/mA = 19 cmx = 17 cm
U = J
6.Hard
3.4 kgk = 260 N/mA = 10 cm

A 3.4 kg mass on a spring with k = 260 N/m is pulled 10 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.4 kgk = 260 N/mA = 10 cm
amax = m/s²

Answer key

  1. 1. k = 428.1 N/m
  2. 2. k = 46.86 N/m
  3. 3. x = −12.67 cm
  4. 4. T = 2.537 s
  5. 5. U = 6.936 J
  6. 6. amax = 7.647 m/s²

Full step-by-step solutions: practise this topic on examproblems.com.