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
4.1 kgk = 340 N/m

A 4.1 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.1 kgk = 340 N/m
f = Hz
2.Easy
1.1 kgk = 200 N/m

A 1.1 kg mass on a spring with stiffness 200 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.1 kgk = 200 N/m
f = Hz
3.Medium
L = 2.1 m

A simple pendulum has a length of 2.1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.1 mg = 9.81 m/s²
T = s
4.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
5.Hard
t (s)x (cm)t = ?12.6

A body oscillates in simple harmonic motion with period 3.4 s and amplitude 14 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 12.6 cm?

T = 3.4 sA = 14 cmx = 12.6 cm
t = s
6.Hard
2.9 kgk = 470 N/m

A 2.9 kg mass is attached to the lower end of an unstretched vertical spring with k = 470 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2.9 kgk = 470 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. f = 1.449 Hz
  2. 2. f = 2.146 Hz
  3. 3. T = 2.907 s
  4. 4. L = 1.315 m
  5. 5. t = 0.6059 s
  6. 6. vmax = 0.7706 m/s

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