What do b and n signify in the damped harmonic motion equation?

AI Thread Summary
In the context of damped harmonic motion, the equation T = b.A^n describes the relationship between the time taken for amplitude to halve (T) and the area of the damper (A). The parameter b signifies the time required for the amplitude to halve when the damper's area is 1. The parameter n indicates how the time taken to halve the amplitude decreases as the damper's area increases, reflecting the sensitivity of the system to changes in damper size. This relationship highlights the impact of damper area on oscillation behavior. Understanding these parameters is crucial for analyzing the effects of damping in harmonic motion.
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Homework Statement



Concerning damped harmonic motion (mass on a spring using cardboard discs as dampers); for the equation (below) of the graph describing the effect of different sized dampers on the time taken for amplitude of oscillations to halve, what do b (y-intercept) and n (gradient) represent? (A=area of damper; T=time taken for amplitude to halve)

Homework Equations



T=b.A^n
(i.e. ln(T)=n.ln(A) + ln(b) )
 
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The Attempt at a Solution b represents the time taken for the amplitude to halve when the area of the damper is equal to 1. n represents the rate at which the time taken for the amplitude to halve decreases as the area of the damper increases.
 

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