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
2.6 kgk10.5 cm

Hanging a 2.6 kg mass on a spring stretches it by 10.5 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 2.6 kgx = 10.5 cmg = 9.81 m/s²
T = s
2.Easy
2.9 kgk = 330 N/m

A 2.9 kg mass on a spring with stiffness 330 N/m oscillates on a frictionless surface. Find the period T.

m = 2.9 kgk = 330 N/m
T = s
3.Medium
t (s)x (cm)1.15 s

A 0.5 kg mass on a spring with k = 20 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 = 1.15 s (with sign).

m = 0.5 kgk = 20 N/mA = 10 cmt = 1.15 s
x = cm
4.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
5.Hard
t (s)x (cm)t = ?2.4

A body oscillates in simple harmonic motion with period 0.7 s and amplitude 8 cm. What is the shortest time t it needs to move from its maximum displacement of 8 cm to a displacement of 2.4 cm?

T = 0.7 sA = 8 cmx = 2.4 cm
t = s
6.Hard
1.3 kgk = 190 N/m

A 1.3 kg mass is attached to the lower end of an unstretched vertical spring with k = 190 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 1.3 kgk = 190 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. T = 0.65 s
  2. 2. T = 0.589 s
  3. 3. x = 5.486 cm
  4. 4. L = 1.553 m
  5. 5. t = 0.1411 s
  6. 6. vmax = 0.8115 m/s

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