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
0.9 kgk = ?5.5 cm

Hanging a 0.9 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 = 0.9 kgx = 5.5 cmg = 9.81 m/s²
k = N/m
2.Easy
2.2 kgk = 170 N/m

A 2.2 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.2 kgk = 170 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 0.8 s? Use g = 9.81 m/s². Find L.

T = 0.8 sg = 9.81 m/s²
L = m
4.Medium
L = 2.8 m

A simple pendulum has a length of 2.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.8 mg = 9.81 m/s²
T = s
5.Hard
1.6 kgk = 260 N/m

A 1.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 260 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 1.6 kgk = 260 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
0.7 kgk = 320 N/mA = 6 cm

A 0.7 kg mass on a spring with k = 320 N/m is pulled 6 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.7 kgk = 320 N/mA = 6 cm
E = J

Answer key

  1. 1. k = 160.5 N/m
  2. 2. f = 1.399 Hz
  3. 3. L = 0.159 m
  4. 4. T = 3.357 s
  5. 5. vmax = 0.7696 m/s
  6. 6. E = 0.576 J

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