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
3.5 kgk = 130 N/m

A 3.5 kg mass on a spring with stiffness 130 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.5 kgk = 130 N/m
f = Hz
2.Easy
1.7 kgk = ?

A 1.7 kg mass on a spring makes 40 complete oscillations in 13 s. Find the spring stiffness k.

m = 1.7 kgN = 40t = 13 s
k = N/m
3.Medium
1.6 kgk = 460 N/mA = 5 cmx = 2 cm

A 1.6 kg mass on a spring with k = 460 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find its speed v when it is 2 cm from equilibrium.

m = 1.6 kgk = 460 N/mA = 5 cmx = 2 cm
v = m/s
4.Medium
L = 0.6 mT = 1.45 s

An astronaut on another planet finds that a simple pendulum 0.6 m long has a period of 1.45 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.6 mT = 1.45 s
g = m/s²
5.Hard
3.1 kgk = 490 N/mA = 8 cm

A 3.1 kg mass on a spring with k = 490 N/m is pulled 8 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.1 kgk = 490 N/mA = 8 cm
amax = m/s²
6.Hard
0.7 kgk = 150 N/mA = 6 cm

A 0.7 kg mass on a spring with k = 150 N/m is pulled 6 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.7 kgk = 150 N/mA = 6 cm
E = J

Answer key

  1. 1. f = 0.97 Hz
  2. 2. k = 635.4 N/m
  3. 3. v = 0.777 m/s
  4. 4. g = 11.27 m/s²
  5. 5. amax = 12.65 m/s²
  6. 6. E = 0.27 J

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