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
3.5 kgk = 50 N/m

A 3.5 kg mass on a spring with stiffness 50 N/m oscillates on a frictionless surface. Find the period T.

m = 3.5 kgk = 50 N/m
T = s
2.Easy
2.5 kgk8.5 cm

Hanging a 2.5 kg mass on a spring stretches it by 8.5 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 = 2.5 kgx = 8.5 cmg = 9.81 m/s²
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.3 s? Use g = 9.81 m/s². Find L.

T = 2.3 sg = 9.81 m/s²
L = m
4.Medium
1.2 kgk = 430 N/mA = 20 cmx = 17 cm

A 1.2 kg mass on a spring with k = 430 N/m oscillates on a frictionless surface with an amplitude of 20 cm. Find its speed v when it is 17 cm from equilibrium.

m = 1.2 kgk = 430 N/mA = 20 cmx = 17 cm
v = m/s
5.Hard
t (s)x (cm)t = ?2

A body oscillates in simple harmonic motion with period 1.5 s and amplitude 8 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 2 cm?

T = 1.5 sA = 8 cmx = 2 cm
t = s
6.Hard
0.6 kgk = 160 N/mA = 12 cm

A 0.6 kg mass on a spring with k = 160 N/m is pulled 12 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.6 kgk = 160 N/mA = 12 cm
E = J

Answer key

  1. 1. T = 1.662 s
  2. 2. T = 0.5849 s
  3. 3. L = 1.315 m
  4. 4. v = 1.994 m/s
  5. 5. t = 0.06032 s
  6. 6. E = 1.152 J

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