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 = 390 N/m

A 1.5 kg mass on a spring with stiffness 390 N/m oscillates on a frictionless surface. Find the period T.

m = 1.5 kgk = 390 N/m
T = s
2.Easy
4.6 kgk = 70 N/m

A 4.6 kg mass on a spring with stiffness 70 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.6 kgk = 70 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
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
3.8 kgk = 90 N/mA = 8 cm

A 3.8 kg mass on a spring with k = 90 N/m is pulled 8 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.8 kgk = 90 N/mA = 8 cm
amax = m/s²
6.Hard
mk = 300 N/mA = 15 cmx = 12 cm

A mass on a spring with k = 300 N/m oscillates on a frictionless surface with an amplitude of 15 cm. Find its kinetic energy K when it is 12 cm from equilibrium.

k = 300 N/mA = 15 cmx = 12 cm
K = J

Answer key

  1. 1. T = 0.3897 s
  2. 2. f = 0.6209 Hz
  3. 3. L = 0.8051 m
  4. 4. T = 3.042 s
  5. 5. amax = 1.895 m/s²
  6. 6. K = 1.215 J

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