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
2.8 kgk = ?

A 2.8 kg mass on a spring oscillates with a period of 1.45 s. Find the spring stiffness k.

m = 2.8 kgT = 1.45 s
k = N/m
2.Easy
3.8 kgk = 170 N/m

A 3.8 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the period T.

m = 3.8 kgk = 170 N/m
T = s
3.Medium
t (s)x (cm)1.45 s

A 0.7 kg mass on a spring with k = 370 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 = 1.45 s (with sign).

m = 0.7 kgk = 370 N/mA = 5 cmt = 1.45 s
x = cm
4.Medium
L = 2 mT = 2.66 s

An astronaut on another planet finds that a simple pendulum 2 m long has a period of 2.66 s for small swings. Find the gravitational acceleration g on that planet.

L = 2 mT = 2.66 s
g = m/s²
5.Hard
2 kgk = 600 N/m300 m/s

A 20 g bullet moving at 300 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 600 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 300 m/sM = 2 kgk = 600 N/m
A = cm
6.Hard
0.6 kgk = 310 N/mA = 2 cm

A 0.6 kg mass on a spring with k = 310 N/m is pulled 2 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.6 kgk = 310 N/mA = 2 cm
vmax = m/s

Answer key

  1. 1. k = 52.58 N/m
  2. 2. T = 0.9394 s
  3. 3. x = −1.713 cm
  4. 4. g = 11.16 m/s²
  5. 5. A = 17.23 cm
  6. 6. vmax = 0.4546 m/s

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