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Study Only (Not to be answered) Write an expression for period, T as a function

ID: 1473160 • Letter: S

Question

Study Only (Not to be answered) Write an expression for period, T as a function of mass, m and spring constant, k using the following equations omega = square root k/m omega = 2pi f What is the angular frequency, omega (rads^-1) of a 100 g mass on a spring with spring constant, K = 20 Nm^-1? Predict the period of oscillation, T(s) of this mass on a spring system. A standing wave on a string is produced when one end is fixed and the other is driven by a 100 Hz oscillator. Three segments are observed as shown below. If the string has a linear mass density, mu of 0.1965 gm^-1 and is under 0.49 N of tension, tau what is the total length of the string in meters? Nu = f lambda = square root tau/mu

Explanation / Answer

1. W = sqrt(k/m) -----------(1)

W=2f --------------(2)

T = 1/f    --------------(3)

Plugging (3) in (1)

W= 2*1/T

T = 2/w = 2*sqrt(m/k)

When m= 0.1kg , k = 20 N/m

W = sqrt(k/m) = sqrt(20/0.1) = 14.14 rad/s

T = 2/w = 2*sqrt(m/k) = (2*3.14)*sqrt(0.1/20) =  0.44s

2.

v= f* = sqrt(T/) -----------(1)

n=3

L= n/2* = 3/2

= 2L/3 ---------(2)

From (1) and (2)

f= [sqrt(T/)]/ = [sqrt(0.49/0.1965)]/(2L/3)  

100 = [sqrt(0.49/0.1965)]/(2L/3)      =>  L = 0.024m = 2.4cm