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
3.3 kgk = ?

A 3.3 kg mass on a spring makes 25 complete oscillations in 48 s. Find the spring stiffness k.

m = 3.3 kgN = 25t = 48 s
k = N/m
2.Easy
4.8 kgk = 150 N/m

A 4.8 kg mass on a spring with stiffness 150 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.8 kgk = 150 N/m
f = Hz
3.Medium
L = 1.5 mT = 3.99 s

An astronaut on another planet finds that a simple pendulum 1.5 m long has a period of 3.99 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.5 mT = 3.99 s
g = m/s²
4.Medium
L = 2.3 m

A simple pendulum has a length of 2.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.3 mg = 9.81 m/s²
T = s
5.Hard
1.4 kgk = 420 N/mA = 9 cm

A 1.4 kg mass on a spring with k = 420 N/m is pulled 9 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.4 kgk = 420 N/mA = 9 cm
vmax = m/s
6.Hard
3.6 kgk = 170 N/mA = 13 cm

A 3.6 kg mass on a spring with k = 170 N/m is pulled 13 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.6 kgk = 170 N/mA = 13 cm
amax = m/s²

Answer key

  1. 1. k = 35.34 N/m
  2. 2. f = 0.8897 Hz
  3. 3. g = 3.72 m/s²
  4. 4. T = 3.042 s
  5. 5. vmax = 1.559 m/s
  6. 6. amax = 6.139 m/s²

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