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
4.8 kgk = 70 N/m

A 4.8 kg mass on a spring with stiffness 70 N/m oscillates on a frictionless surface. Find the period T.

m = 4.8 kgk = 70 N/m
T = s
2.Easy
0.4 kgk = 170 N/m

A 0.4 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the period T.

m = 0.4 kgk = 170 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.5 s? Use g = 9.81 m/s². Find L.

T = 2.5 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.9 s? Use g = 9.81 m/s². Find L.

T = 1.9 sg = 9.81 m/s²
L = m
5.Hard
0.6 kgk = 230 N/mA = 19 cm

A 0.6 kg mass on a spring with k = 230 N/m is pulled 19 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.6 kgk = 230 N/mA = 19 cm
E = J
6.Hard
t (s)x (cm)t = ?13.5

A body oscillates in simple harmonic motion with period 3.6 s and amplitude 15 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 13.5 cm?

T = 3.6 sA = 15 cmx = 13.5 cm
t = s

Answer key

  1. 1. T = 1.645 s
  2. 2. T = 0.3048 s
  3. 3. L = 1.553 m
  4. 4. L = 0.897 m
  5. 5. E = 4.152 J
  6. 6. t = 0.6416 s

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