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
4.7 kgk = 60 N/m

A 4.7 kg mass on a spring with stiffness 60 N/m oscillates on a frictionless surface. Find the period T.

m = 4.7 kgk = 60 N/m
T = s
2.Easy
3.8 kgk = ?

A 3.8 kg mass on a spring oscillates with a period of 1.45 s. Find the spring stiffness k.

m = 3.8 kgT = 1.45 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.8 s? Use g = 9.81 m/s². Find L.

T = 2.8 sg = 9.81 m/s²
L = m
4.Medium
L = 1.2 mT = 5.41 s

An astronaut on another planet finds that a simple pendulum 1.2 m long has a period of 5.41 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.2 mT = 5.41 s
g = m/s²
5.Hard
3.5 kgk = 120 N/mA = 9 cm

A 3.5 kg mass on a spring with k = 120 N/m is pulled 9 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.5 kgk = 120 N/mA = 9 cm
vmax = m/s
6.Hard
3.7 kgk = 420 N/mA = 6 cm

A 3.7 kg mass on a spring with k = 420 N/m is pulled 6 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.7 kgk = 420 N/mA = 6 cm
amax = m/s²

Answer key

  1. 1. T = 1.759 s
  2. 2. k = 71.35 N/m
  3. 3. L = 1.948 m
  4. 4. g = 1.619 m/s²
  5. 5. vmax = 0.527 m/s
  6. 6. amax = 6.811 m/s²

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