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Simple Harmonic Motion

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Lab Activities

This lab looks at two situations for a mechanical harmonic oscillator: undamped oscillations and damped oscillations. The system is a car on a horizontal air track attached to the ends of the air track by springs.

For the undamped case, the students do the following:

a. check to see if the period of oscillation is independent of the initial displacement of the car from its equilibrium position;

b. measure the natural oscillating frequency of the car; and

c. measure the spring constants of the springs and the mass of the car and from that data compute a theoretical value for the natural oscillating frequency; comparison is made between the value measured in part (b) and the value computed in part (c).

For the damped case, the students measure the damping constant. Damping is achieved by mounting an aluminum sail on the car and passing it through the poles of a magnet. The separation of the poles can be manually varied to change the amount of damping.

A third part is available. In this part, two cars are used with the cars connected to each other by a weak spring and each connected to one end of the track by stiffer springs. The frequency of oscillation of the symmetrical and anti-symmetrical modes are measured and compared to theory. Also observed is a motion of the system which is a linear combination of the symmetrical and anti-symmetrical mode. In this case one car is held at its equilibrium position while the other is displaced from its equilibrium position. The resulting motion is a combination of the quick oscillation of the individual cars and the slower oscillation of the energy transfer between the two cars. Both frequencies are measured and compared to theory.

Course Level

Introductory:

Student Handouts

Equipment

Number of set-ups available: 10

Per lab station:

1 airtrack/connecting hose and wooden dust cover
1 air cart/1 aluminum sail
2 5 cm springs
1 stopwatch
1 damping magnet
1 ringstand/bar
2 ring stand clamps
1 balance/standard mass set

General class supplies: (Not shown)

spring constant apparatus consisting of:
2 metersticks
1 C-Clamp
4 bars
3 ring stand clamps
2 hooked rings
1 air supply per 3 tracks
1 hooked mass set ( 2 - 200g, 2 100g, 2 - 50g, 2 - 20g, 2 - 10g)

apparatus

Notes


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