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 kgk = ?24 cm

Hanging a 2 kg mass on a spring stretches it by 24 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2 kgx = 24 cmg = 9.81 m/s²
k = N/m
2.Easy
0.5 kgk = 90 N/m

A 0.5 kg mass on a spring with stiffness 90 N/m oscillates on a frictionless surface. Find the period T.

m = 0.5 kgk = 90 N/m
T = s
3.Medium
L = 2.5 m

A simple pendulum has a length of 2.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.5 mg = 9.81 m/s²
T = s
4.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
5.Hard
1.1 kgk = 30 N/mA = 5 cm

A 1.1 kg mass on a spring with k = 30 N/m is pulled 5 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.1 kgk = 30 N/mA = 5 cm
E = J
6.Hard
t (s)x (cm)t = ?7.2

A body oscillates in simple harmonic motion with period 1.8 s and amplitude 9 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 7.2 cm?

T = 1.8 sA = 9 cmx = 7.2 cm
t = s

Answer key

  1. 1. k = 81.75 N/m
  2. 2. T = 0.4683 s
  3. 3. T = 3.172 s
  4. 4. L = 0.4199 m
  5. 5. E = 0.0375 J
  6. 6. t = 0.2657 s

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