Question

True or False: The linear oscillator's period is measured by averaging over ten cycles. Explains Why True or False?

Answer 1

linear oscillator is the oscilation where the system has only one degree of freedom.

now consider a pendulum for example.

its time period is given by T=2*pi*sqrt(l/g)

where l=length of the pendulum

g=9.8 m/s^2

let the length of the pendulum be 0.5 m.

then time period=2*pi*sqrt(0.5/9.8)=1.4192 seconds

as in any measurement, human error is unavoidable upto certain extent and in this case, we have to determine the starting and end point of a single complete cycle accurately, error is bound to show up in time measurement.

hence by taking multiple measurements and taking the final value as average of all the measurement values, we will be able to decrease the error magnitude to an acceptabale value.

hence usually 10 or 20 oscillations are taken and then average time period is used for further calculations.