An oscillator with a mass of and a period of has
an amplitude that decreases by during each complete oscillation.
If the initial amplitude is , what will be the amplitude
The amplitude after oscillation is
Damping oscillation: The mechanical energy in a real oscillating system decreases during oscillation because external forces, such as resistance, prevent the oscillation and convert the mechanical energy into thermal energy. The real oscillator and its movement are then said to be damped. If the damping force gives , where v is the speed of the oscillation and b is the damping constant, then the displacement of the oscillation is given by
where , the angular frequency of the damped oscillator can be given by
now is the angular frequency of an undamped oscillator
The objective is to find out the amplitude of the oscillator after oscillations
Since, The amplitude of the oscillation decreases by after a complete oscillation, the amplitude after the first oscillation is
where is the initial amplitude of the oscillation. The amplitude after second oscillation is
The amplitude of the oscillator after oscillations is
Your lab instructor has asked you to measure a spring constant using a dynamic method—letting it oscillate—rather than a static method of stretching it. You and your lab partner suspend the spring from a hook, hang different masses on the lower end, and start them oscillating. One of you uses a meter stick to measure the amplitude, the other uses a stopwatch to time oscillations.
Your data are as follows:
Use the best-fit line of an appropriate graph to determine the spring constant.
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