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
2.4 kgk = 320 N/m

A 2.4 kg mass on a spring with stiffness 320 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.4 kgk = 320 N/m
f = Hz
2.Easy
2 kgk = ?

A 2 kg mass on a spring oscillates with a period of 1.25 s. Find the spring stiffness k.

m = 2 kgT = 1.25 s
k = N/m
3.Medium
2.7 kgk = 450 N/mA = 10 cmx = 7 cm

A 2.7 kg mass on a spring with k = 450 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find its speed v when it is 7 cm from equilibrium.

m = 2.7 kgk = 450 N/mA = 10 cmx = 7 cm
v = m/s
4.Medium
L = 1 m

A simple pendulum has a length of 1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1 mg = 9.81 m/s²
T = s
5.Hard
t (s)x (cm)t = ?4.5

A body oscillates in simple harmonic motion with period 2.9 s and amplitude 15 cm. What is the shortest time t it needs to move from its maximum displacement of 15 cm to a displacement of 4.5 cm?

T = 2.9 sA = 15 cmx = 4.5 cm
t = s
6.Hard
2.6 kgk = 280 N/m

A 2.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 280 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2.6 kgk = 280 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. f = 1.838 Hz
  2. 2. k = 50.53 N/m
  3. 3. v = 0.922 m/s
  4. 4. T = 2.006 s
  5. 5. t = 0.5844 s
  6. 6. vmax = 0.9453 m/s

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