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
1.8 kgk = 90 N/m

A 1.8 kg mass on a spring with stiffness 90 N/m oscillates on a frictionless surface. Find the period T.

m = 1.8 kgk = 90 N/m
T = s
2.Easy
4 kgk = ?

A 4 kg mass on a spring oscillates with a period of 0.55 s. Find the spring stiffness k.

m = 4 kgT = 0.55 s
k = N/m
3.Medium
t (s)x (cm)1.25 s

A 3.4 kg mass on a spring with k = 290 N/m is pulled 10 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.25 s (with sign).

m = 3.4 kgk = 290 N/mA = 10 cmt = 1.25 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.9 s? Use g = 9.81 m/s². Find L.

T = 2.9 sg = 9.81 m/s²
L = m
5.Hard
2.8 kgk = 140 N/mA = 14 cm

A 2.8 kg mass on a spring with k = 140 N/m is pulled 14 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.8 kgk = 140 N/mA = 14 cm
amax = m/s²
6.Hard
0.4 kgk = 350 N/m

A 0.4 kg mass is attached to the lower end of an unstretched vertical spring with k = 350 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 0.4 kgk = 350 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. T = 0.8886 s
  2. 2. k = 522 N/m
  3. 3. x = 5.216 cm
  4. 4. L = 2.09 m
  5. 5. amax = 7 m/s²
  6. 6. xmax = 2.242 cm

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