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 kgk = 250 N/m

A 1 kg mass on a spring with stiffness 250 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1 kgk = 250 N/m
f = Hz
2.Easy
3.8 kgk = ?

A 3.8 kg mass on a spring oscillates with a period of 2.15 s. Find the spring stiffness k.

m = 3.8 kgT = 2.15 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 3 s? Use g = 9.81 m/s². Find L.

T = 3 sg = 9.81 m/s²
L = m
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
2.4 kgk = 300 N/m

A 2.4 kg mass is attached to the lower end of an unstretched vertical spring with k = 300 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2.4 kgk = 300 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
t (s)x (cm)t = ?8.4

A body oscillates in simple harmonic motion with period 3.3 s and amplitude 12 cm. What is the shortest time t it needs to move from its maximum displacement of 12 cm to a displacement of 8.4 cm?

T = 3.3 sA = 12 cmx = 8.4 cm
t = s

Answer key

  1. 1. f = 2.516 Hz
  2. 2. k = 32.45 N/m
  3. 3. L = 2.236 m
  4. 4. T = 3.172 s
  5. 5. vmax = 0.8774 m/s
  6. 6. t = 0.4178 s

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