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
2.3 kgk = ?

A 2.3 kg mass on a spring makes 40 complete oscillations in 27 s. Find the spring stiffness k.

m = 2.3 kgN = 40t = 27 s
k = N/m
2.Easy
2.3 kgk

A 2.3 kg mass on a spring makes 30 complete oscillations in 27 s. Find the frequency f of the oscillation.

m = 2.3 kgN = 30t = 27 s
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.6 s? Use g = 9.81 m/s². Find L.

T = 1.6 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2 s? Use g = 9.81 m/s². Find L.

T = 2 sg = 9.81 m/s²
L = m
5.Hard
t (s)x (cm)t = ?6

A body oscillates in simple harmonic motion with period 2.1 s and amplitude 8 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 6 cm?

T = 2.1 sA = 8 cmx = 6 cm
t = s
6.Hard
3.2 kgk = 200 N/mA = 10 cm

A 3.2 kg mass on a spring with k = 200 N/m is pulled 10 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.2 kgk = 200 N/mA = 10 cm
E = J

Answer key

  1. 1. k = 199.3 N/m
  2. 2. f = 1.111 Hz
  3. 3. L = 0.6361 m
  4. 4. L = 0.994 m
  5. 5. t = 0.2834 s
  6. 6. E = 1 J

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