To use a spring to test Hooke’s law and to study simple harmonic motion.
Vibrating spring apparatus consisting of stand, spring, weight hanger, set of slotted
(20 to 200 g), balance, stopwatch
When an elastic body is distorted by some externally applied force, a restoring
force is produced in the body which is directly proportional to the amount of
distortion caused. The relation between the restoring force F and the distortion x is F = kx.
This is known as Hooke’s law and the constant k is called the force constant of the spring.
The period of vibration of a mass hanging from a vertical spring when set in
simple harmonic motion is
T is the period of oscillation in seconds,
m is the mass of the vibrating system in kg,
k is the force constant of the spring in units of N/m.
Remove the spring from the weight hanger and determine its mass
in grams by weighing it on the balance to the nearest 0.1 g.
Weigh the weight hanger and record its mass in grams.
Reattach the spring to the weight hanger, suspend it from the
support and adjust the scale position so that the pointer on
the weight hanger reads zero on the scale.
Place 20 g on the weight hanger and record the position of the pointer on the scale.
Repeat procedure (4) with loads of 40 to 200 g in steps of 20 g in each case recording the
position of the pointer on the scale.
Remove the 100 g from the weight hanger so that it now has only 100 g on it.
Displace the weight hanger downwards about 1 cm from its equilibrium position and set it in
vertical oscillation. Using the stopwatch, measure the time taken for 25 complete
oscillations and record it. Remember to count zero when you let go of the mass.
Repeat procedure (6) with the same mass but now displace it 2 cm. Again measure the time
for 25 oscillations and record its value.
Now add an additional 50 g to the weight hanger,
displace it 1 cm and time 25 complete oscillations.
For each set of data calculate the total mass suspended from the spring by adding
the mass of the hanger to the added mass and calculate the stretching force in N from
grams x 0.0098.
Plot a graph of the values of the total stretching force in N (on the y-axis) versus the corresponding
value of the scale reading in cm (on the x-axis). The slope of the graph gives the force constant of
the spring k in N/cm. Convert this to N/m by multiplying by 100 and enter the value
in the table.
From the data in procedures (6) through (8) calculate the experimental values of
the period (the time for one oscillation) and record the values in the table.
Use the equation to calculate the values
of the theoretical period. (m is the mass of the vibrating system which is the weight hanger, plus
the added mass, plus 1/3 the mass of the spring) and k is the slope of the graph in N/m.
Calculate the percent error between the experimental and theoretical values of the
period using the relation
Percent error =
Mass of spring = ________ g Mass of weight hanger = ________ g
Mass added to weight hanger in g
Total mass suspended from spring in g
Total stretching force in N (kg x 9.81)
Scale reading in cm
Force constant of spring = ________ N/m
Mass added to weight hanger in g
Effective mass of vibrating system in g
Amplitude of vibration in cm
Time for 25 vibrations in seconds
Experimental value of period in seconds
Theoretical value of period in seconds
What does your graph show about the dependence of the elongation of the spring on
the applied force? Does this verify Hooke’s Law?
At what point does the vibrating mass have
(a) greatest acceleration
(b) least acceleration
(c) greatest velocity
(d) least velocity
(e) greatest kinetic energy
(f) least kinetic energy ?
Is the motion of the piston in a gasoline or steam engine simple harmonic motion?
Explain your answer by comparison to the vibration of a mass on a spring.
What can you deduce about the effect of the amplitude of vibration on the period
of oscillation from the measurements that you took in this experiment?
Is this what you expected? If not - why not?
Calculate the value of the mass in grams that you would need for your vibrating
system to have a period of oscillation of exactly one second.
If the frequency of oscillation of a 405 g mass on a
certain spring is 2.5 Hz, what is the value of the spring constant in N/cm?