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 = ?

A 2 kg mass on a spring makes 20 complete oscillations in 46 s. Find the spring stiffness k.

m = 2 kgN = 20t = 46 s
k = N/m
2.Easy
0.3 kgk5.5 cm

Hanging a 0.3 kg mass on a spring stretches it by 5.5 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 = 0.3 kgx = 5.5 cmg = 9.81 m/s²
T = s
3.Medium
1.7 kgk = 340 N/mA = 10 cmx = 6 cm

A 1.7 kg mass on a spring with k = 340 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find its speed v when it is 6 cm from equilibrium.

m = 1.7 kgk = 340 N/mA = 10 cmx = 6 cm
v = m/s
4.Medium
L = 2.5 m

A simple pendulum has a length of 2.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.5 mg = 9.81 m/s²
T = s
5.Hard
0.3 kgk = 450 N/mA = 19 cm

A 0.3 kg mass on a spring with k = 450 N/m is pulled 19 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.3 kgk = 450 N/mA = 19 cm
vmax = m/s
6.Hard
t (s)x (cm)t = ?8.1

A body oscillates in simple harmonic motion with period 2.2 s and amplitude 9 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 8.1 cm?

T = 2.2 sA = 9 cmx = 8.1 cm
t = s

Answer key

  1. 1. k = 14.93 N/m
  2. 2. T = 0.4705 s
  3. 3. v = 1.131 m/s
  4. 4. T = 3.172 s
  5. 5. vmax = 7.359 m/s
  6. 6. t = 0.3921 s

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