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CHAPTER 9 : APPLICATIONS

9.1 The Expression A sin wt + B cos wt

The equation y = A sin wt + B cos wt .........(1)

Put A = a cos a and B = a sin a in equation (1) we get

y = ( a cos a ) sin wt + (a sin a) cos wt

y = a [ sin wt cos a + cos wt sin a]

y = a sin (wt + a) ........(2)

The two equations (1) and (2) are equivalent expressions.

and Asin wt + Bcos wt = a sin (wt + a) given that 'a' is an angle with a point P (A, B) on its terminal side.

Example 1 Transform y = 3 sin 2t + 4 cos 2t to the form y = a sin (wt + a). Also find period, amplitude, frequency and phase shift.

Solution

y = 3 sin 2t + 4 cos 2t. Comparing with y = A sin wt + B cos wt, we get A = 3, B = 4 and w = 2.

Example 2 Convert y = sin p t + cos p t to the form y = a sin (wt + a). Also find its period, frequency, amplitude and phase shift.

Solution

Index

9.1 The Expression A sin wt + B coswt
9.2 Simple Harmonic Motion

Chapter 1

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