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
1.2 kgk = 230 N/m

A 1.2 kg mass on a spring with stiffness 230 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.2 kgk = 230 N/m
f = Hz
2.Easy
1.3 kgk24 cm

Hanging a 1.3 kg mass on a spring stretches it by 24 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 = 1.3 kgx = 24 cmg = 9.81 m/s²
T = s
3.Medium
L = 0.8 m

A simple pendulum has a length of 0.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.8 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 0.9 s? Use g = 9.81 m/s². Find L.

T = 0.9 sg = 9.81 m/s²
L = m
5.Hard
2.8 kgk = 430 N/mA = 11 cm

A 2.8 kg mass on a spring with k = 430 N/m is pulled 11 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.8 kgk = 430 N/mA = 11 cm
amax = m/s²
6.Hard
1.3 kgk = 310 N/mA = 13 cm

A 1.3 kg mass on a spring with k = 310 N/m is pulled 13 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.3 kgk = 310 N/mA = 13 cm
E = J

Answer key

  1. 1. f = 2.203 Hz
  2. 2. T = 0.9828 s
  3. 3. T = 1.794 s
  4. 4. L = 0.2013 m
  5. 5. amax = 16.89 m/s²
  6. 6. E = 2.62 J

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