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
0.7 kgk = 390 N/m

A 0.7 kg mass on a spring with stiffness 390 N/m oscillates on a frictionless surface. Find the period T.

m = 0.7 kgk = 390 N/m
T = s
2.Easy
3.9 kgk = 150 N/m

A 3.9 kg mass on a spring with stiffness 150 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.9 kgk = 150 N/m
f = Hz
3.Medium
L = 1.8 mT = 1.69 s

An astronaut on another planet finds that a simple pendulum 1.8 m long has a period of 1.69 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.8 mT = 1.69 s
g = m/s²
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 = ?7.6

A body oscillates in simple harmonic motion with period 3.7 s and amplitude 19 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 7.6 cm?

T = 3.7 sA = 19 cmx = 7.6 cm
t = s
6.Hard
3.5 kgk = 270 N/mA = 6 cm

A 3.5 kg mass on a spring with k = 270 N/m is pulled 6 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.5 kgk = 270 N/mA = 6 cm
vmax = m/s

Answer key

  1. 1. T = 0.2662 s
  2. 2. f = 0.987 Hz
  3. 3. g = 24.88 m/s²
  4. 4. L = 0.994 m
  5. 5. t = 0.2423 s
  6. 6. vmax = 0.527 m/s

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