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
1.3 kgk = 360 N/m

A 1.3 kg mass on a spring with stiffness 360 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.3 kgk = 360 N/m
f = Hz
2.Easy
1.7 kgk = 340 N/m

A 1.7 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.7 kgk = 340 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.7 s? Use g = 9.81 m/s². Find L.

T = 2.7 sg = 9.81 m/s²
L = m
4.Medium
L = 2.9 m

A simple pendulum has a length of 2.9 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.9 mg = 9.81 m/s²
T = s
5.Hard
3 kgk = 220 N/m

A 3 kg mass is attached to the lower end of an unstretched vertical spring with k = 220 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 3 kgk = 220 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
t (s)x (cm)t = ?14

A body oscillates in simple harmonic motion with period 3.9 s and amplitude 20 cm. What is the shortest time t it needs to move from its maximum displacement of 20 cm to a displacement of 14 cm?

T = 3.9 sA = 20 cmx = 14 cm
t = s

Answer key

  1. 1. f = 2.648 Hz
  2. 2. f = 2.251 Hz
  3. 3. L = 1.811 m
  4. 4. T = 3.416 s
  5. 5. vmax = 1.146 m/s
  6. 6. t = 0.4937 s

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