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
1.1 kgk8 cm

Hanging a 1.1 kg mass on a spring stretches it by 8 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 1.1 kgx = 8 cmg = 9.81 m/s²
T = s
2.Easy
1.2 kgk = ?

A 1.2 kg mass on a spring oscillates with a period of 1.6 s. Find the spring stiffness k.

m = 1.2 kgT = 1.6 s
k = N/m
3.Medium
L = 2 m

A simple pendulum has a length of 2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2 mg = 9.81 m/s²
T = s
4.Medium
L = 1.3 m

A simple pendulum has a length of 1.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.3 mg = 9.81 m/s²
T = s
5.Hard
0.3 kgk = 100 N/mA = 4 cm

A 0.3 kg mass on a spring with k = 100 N/m is pulled 4 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.3 kgk = 100 N/mA = 4 cm
E = J
6.Hard
3 kgk = 100 N/mA = 17 cm

A 3 kg mass on a spring with k = 100 N/m is pulled 17 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3 kgk = 100 N/mA = 17 cm
amax = m/s²

Answer key

  1. 1. T = 0.5674 s
  2. 2. k = 18.51 N/m
  3. 3. T = 2.837 s
  4. 4. T = 2.287 s
  5. 5. E = 0.08 J
  6. 6. amax = 5.667 m/s²

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