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
2.7 kgk9 cm

Hanging a 2.7 kg mass on a spring stretches it by 9 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 = 2.7 kgx = 9 cmg = 9.81 m/s²
T = s
2.Easy
0.5 kgk = ?

A 0.5 kg mass on a spring oscillates with a period of 2.4 s. Find the spring stiffness k.

m = 0.5 kgT = 2.4 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.3 s? Use g = 9.81 m/s². Find L.

T = 1.3 sg = 9.81 m/s²
L = m
4.Medium
L = 0.5 m

A simple pendulum has a length of 0.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.5 mg = 9.81 m/s²
T = s
5.Hard
0.5 kgk = 600 N/m300 m/s

A 15 g bullet moving at 300 m/s hits and stays in a 0.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 600 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 300 m/sM = 0.5 kgk = 600 N/m
A = cm
6.Hard
2 kgk = 430 N/m

A 2 kg mass is attached to the lower end of an unstretched vertical spring with k = 430 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2 kgk = 430 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. T = 0.6018 s
  2. 2. k = 3.427 N/m
  3. 3. L = 0.4199 m
  4. 4. T = 1.419 s
  5. 5. A = 25.6 cm
  6. 6. vmax = 0.669 m/s

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