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
0.5 kgk = ?13 cm

Hanging a 0.5 kg mass on a spring stretches it by 13 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.5 kgx = 13 cmg = 9.81 m/s²
k = N/m
2.Easy
2.3 kgk = 190 N/m

A 2.3 kg mass on a spring with stiffness 190 N/m oscillates on a frictionless surface. Find the period T.

m = 2.3 kgk = 190 N/m
T = s
3.Medium
L = 0.3 m

A simple pendulum has a length of 0.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.3 mg = 9.81 m/s²
T = s
4.Medium
L = 2.3 m

A simple pendulum has a length of 2.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.3 mg = 9.81 m/s²
T = s
5.Hard
1.4 kgk = 340 N/m

A 1.4 kg mass is attached to the lower end of an unstretched vertical spring with k = 340 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 1.4 kgk = 340 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
3 kgk = 150 N/mA = 17 cm

A 3 kg mass on a spring with k = 150 N/m is pulled 17 cm from equilibrium and released. Find its maximum speed vmax.

m = 3 kgk = 150 N/mA = 17 cm
vmax = m/s

Answer key

  1. 1. k = 37.73 N/m
  2. 2. T = 0.6913 s
  3. 3. T = 1.099 s
  4. 4. T = 3.042 s
  5. 5. vmax = 0.6295 m/s
  6. 6. vmax = 1.202 m/s

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