TS EAMCET 03 May 2019 Shift 2 Solved Paper

The expression for the displacement of particle in simple harmonic motion is given by,
x=A‌sin(ωt+φ)
Differentiate the above expression with respect to t
‌

dx

dt

‌‌=Aω‌cos(ωt+φ)
‌‌=Aω[1−sin2(ωt+φ)]

1

2

‌‌=Aω[1−‌

x2

A2

]

1

2

‌‌=ω√A2−x2
It can be written as,
‌

dx

dt

‌‌=ω√A2−x2
‌‌=ω√(−1)(x2−A2)
‌‌=ω√−1√(x2−A2)
‌‌=iω√x2−A2
The above represents simple harmonic motion.