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finding the phase shift

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2 Answers

Amp A = √20
Period T = 1/2 (solving 4piT = 2pi for T.)
Phase shift φ = -7/(4pi e) (solving 4piφ+7/e = 0 for φ.)
Let's compare your equation to that of a general sinusoidal oscillation:
 
y = A sin ((2*Pi/T) x - φ),
 
where A is the amplitude, T the period, and φ the phase shift. You have
 
y = √20 sin ((4*Pi) x + 7e-1),
 
therefore the amplitude is A=√20, the period we get from
 
2*Pi/T = 4*Pi, which gives us T=1/2,
 
and the phase shift is φ=-7e-1.
 
With this information you should be able to sketch the graph of the oscillation.