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
4.7 kgk = ?

A 4.7 kg mass on a spring oscillates with a period of 2.2 s. Find the spring stiffness k.

m = 4.7 kgT = 2.2 s
k = N/m
2.Easy
0.7 kgk = ?16 cm

Hanging a 0.7 kg mass on a spring stretches it by 16 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.7 kgx = 16 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 2.4 m

A simple pendulum has a length of 2.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.4 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
5.Hard
1.3 kgk = 280 N/m

A 1.3 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 = 1.3 kgk = 280 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
t (s)x (cm)t = ?8.1

A body oscillates in simple harmonic motion with period 3.7 s and amplitude 9 cm. What is the shortest time t it needs to move from its maximum displacement of 9 cm to a displacement of 8.1 cm?

T = 3.7 sA = 9 cmx = 8.1 cm
t = s

Answer key

  1. 1. k = 38.34 N/m
  2. 2. k = 42.92 N/m
  3. 3. T = 3.108 s
  4. 4. L = 0.8051 m
  5. 5. vmax = 0.6684 m/s
  6. 6. t = 0.2656 s

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