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
1.5 kgk = 40 N/m

A 1.5 kg mass on a spring with stiffness 40 N/m oscillates on a frictionless surface. Find the period T.

m = 1.5 kgk = 40 N/m
T = s
2.Easy
0.2 kgk = ?

A 0.2 kg mass on a spring oscillates with a period of 0.45 s. Find the spring stiffness k.

m = 0.2 kgT = 0.45 s
k = N/m
3.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
4.Medium
L = 1.7 mT = 2.75 s

An astronaut on another planet finds that a simple pendulum 1.7 m long has a period of 2.75 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.7 mT = 2.75 s
g = m/s²
5.Hard
0.6 kgk = 440 N/m

A 0.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 440 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.6 kgk = 440 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
0.7 kgk = 110 N/mA = 14 cm

A 0.7 kg mass on a spring with k = 110 N/m is pulled 14 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.7 kgk = 110 N/mA = 14 cm
vmax = m/s

Answer key

  1. 1. T = 1.217 s
  2. 2. k = 38.99 N/m
  3. 3. T = 2.287 s
  4. 4. g = 8.874 m/s²
  5. 5. vmax = 0.3623 m/s
  6. 6. vmax = 1.755 m/s

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