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.

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1.Easy
2.7 kgk = 310 N/m

A 2.7 kg mass on a spring with stiffness 310 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.7 kgk = 310 N/m
f = Hz
2.Easy
2 kgk = ?12 cm

Hanging a 2 kg mass on a spring stretches it by 12 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2 kgx = 12 cmg = 9.81 m/s²
k = N/m
3.Medium
t (s)x (cm)1.1 s

A 3.6 kg mass on a spring with k = 160 N/m is pulled 7 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.1 s (with sign).

m = 3.6 kgk = 160 N/mA = 7 cmt = 1.1 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.4 s? Use g = 9.81 m/s². Find L.

T = 2.4 sg = 9.81 m/s²
L = m
5.Hard
0.5 kgk = 400 N/m200 m/s

A 12 g bullet moving at 200 m/s hits and stays in a 0.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 400 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 200 m/sM = 0.5 kgk = 400 N/m
A = cm
6.Hard
0.9 kgk = 300 N/mA = 7 cm

A 0.9 kg mass on a spring with k = 300 N/m is pulled 7 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.9 kgk = 300 N/mA = 7 cm
vmax = m/s

Answer key

  1. 1. f = 1.705 Hz
  2. 2. k = 163.5 N/m
  3. 3. x = 3.482 cm
  4. 4. L = 1.431 m
  5. 5. A = 16.77 cm
  6. 6. vmax = 1.278 m/s

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