What is the form of the equation of motion for the SHM of a mass suspended on a

Question

What is the form of the equation of motion for the SHM of a mass suspended on a spring when the mass is initially (a) released 10 cm above the equilibrium position; (b) given an upward push from the equilibrium position, so that it undergoes a maximum displacement of 8 cm; (c) given a downward push from the equilibrium position, so that it undergoes a maximum displacement of 12 cm? (Hint: Sketch the curve for the motion as in TI Fig. 14.2 and fit the appropriate trigonometric function to the curve.)

Explanation / Answer

We know equation isx(t) =A (coswt +F)

(a)X=10,t=0

10=10(cosw(0)+F)

and there is no initial phase change andF=0

x(t) =10(coswt)

curve is cos curve http://people.wku.edu/tom.richmond/Cosine.html

(b)similarly,for X=0,t=0

X = 8sinwt

curve is sine curve http://people.wku.edu/tom.richmond/Sine.html

(c)similarly,for X=0,t=0

X=12sinwt

curve is sine curve http://people.wku.edu/tom.richmond/Sine.html

Here ,in all casesw=(k/m)1/2

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