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
5 kgk = 380 N/m

A 5 kg mass on a spring with stiffness 380 N/m oscillates on a frictionless surface. Find the period T.

m = 5 kgk = 380 N/m
T = s
2.Easy
3.6 kgk

A 3.6 kg mass on a spring makes 30 complete oscillations in 54 s. Find the frequency f of the oscillation.

m = 3.6 kgN = 30t = 54 s
f = Hz
3.Medium
L = 0.5 mT = 2.3 s

An astronaut on another planet finds that a simple pendulum 0.5 m long has a period of 2.3 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.5 mT = 2.3 s
g = m/s²
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
mk = 70 N/mA = 19 cmx = 1 cm

A mass on a spring with k = 70 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find the energy U stored in the spring when the mass is 1 cm from equilibrium.

k = 70 N/mA = 19 cmx = 1 cm
U = J
6.Hard
3.2 kgk = 270 N/mA = 11 cm

A 3.2 kg mass on a spring with k = 270 N/m is pulled 11 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.2 kgk = 270 N/mA = 11 cm
vmax = m/s

Answer key

  1. 1. T = 0.7207 s
  2. 2. f = 0.5556 Hz
  3. 3. g = 3.731 m/s²
  4. 4. L = 0.2013 m
  5. 5. U = 0.0035 J
  6. 6. vmax = 1.01 m/s

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