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 kgk = 100 N/m

A 2 kg mass on a spring with stiffness 100 N/m oscillates on a frictionless surface. Find the period T.

m = 2 kgk = 100 N/m
T = s
2.Easy
1.7 kgk = 330 N/m

A 1.7 kg mass on a spring with stiffness 330 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.7 kgk = 330 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.4 s? Use g = 9.81 m/s². Find L.

T = 1.4 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)0.45 s

A 1.1 kg mass on a spring with k = 360 N/m is pulled 3 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.45 s (with sign).

m = 1.1 kgk = 360 N/mA = 3 cmt = 0.45 s
x = cm
5.Hard
3.5 kgk = 40 N/mA = 20 cm

A 3.5 kg mass on a spring with k = 40 N/m is pulled 20 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.5 kgk = 40 N/mA = 20 cm
amax = m/s²
6.Hard
2.1 kgk = 490 N/mA = 9 cm

A 2.1 kg mass on a spring with k = 490 N/m is pulled 9 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.1 kgk = 490 N/mA = 9 cm
vmax = m/s

Answer key

  1. 1. T = 0.8886 s
  2. 2. f = 2.217 Hz
  3. 3. L = 0.487 m
  4. 4. x = −0.8487 cm
  5. 5. amax = 2.286 m/s²
  6. 6. vmax = 1.375 m/s

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