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
4.6 kgk = 270 N/m

A 4.6 kg mass on a spring with stiffness 270 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.6 kgk = 270 N/m
f = Hz
2.Easy
0.5 kgk = 20 N/m

A 0.5 kg mass on a spring with stiffness 20 N/m oscillates on a frictionless surface. Find the period T.

m = 0.5 kgk = 20 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.5 s? Use g = 9.81 m/s². Find L.

T = 2.5 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)0.55 s

A 3.7 kg mass on a spring with k = 340 N/m is pulled 5 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.55 s (with sign).

m = 3.7 kgk = 340 N/mA = 5 cmt = 0.55 s
x = cm
5.Hard
t (s)x (cm)t = ?18

A body oscillates in simple harmonic motion with period 1.9 s and amplitude 20 cm. What is the shortest time t it needs to move from its maximum displacement of 20 cm to a displacement of 18 cm?

T = 1.9 sA = 20 cmx = 18 cm
t = s
6.Hard
2.4 kgk = 140 N/mA = 5 cm

A 2.4 kg mass on a spring with k = 140 N/m is pulled 5 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.4 kgk = 140 N/mA = 5 cm
vmax = m/s

Answer key

  1. 1. f = 1.219 Hz
  2. 2. T = 0.9935 s
  3. 3. L = 1.553 m
  4. 4. x = 2.656 cm
  5. 5. t = 0.1364 s
  6. 6. vmax = 0.3819 m/s

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