Solution: Q69 Consider a general equation, x = Acosωt A − a = Acosωt From here, cosωt = A − aASimilarly, A − ( a + 2 a ) = A cos2ωt [ ∴ time doubled] cos2ωt = A − 3 aA cos2θ = 2cos2θ − 1 (A − aA)2= A − 3 a + A2 A From here, A = 2 a So, amplitude of the motion is 2 a 2 a − a = 2acosωt π3= ω t π3= 2 πTτT = 6 τ

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Solution:
Q69.

C o n s i d e r a g e n e r a l e q u a t i o n, x = A c o s ω t A - a = A c o s ω t F r o m h e r e, c o s ω t = \frac{A - a}{A} S i m i l a r l y, A - (a + 2 a) = A c o s 2 ω t [∴ t i m e d o u b l e d] c o s 2 ω t = \frac{A - 3 a}{A} c o s 2 θ = 2 c o s^{2} θ - 1 {(\frac{A - a}{A})}^{2} = \frac{A - 3 a + A}{2 A} F r o m h e r e, A = 2 a S o, a m p l i t u d e o f t h e m o t i o n i s 2 a 2 a - a = 2 a c o s ω t \frac{π}{3} = ω t \frac{π}{3} = \frac{2 π}{T} τ T = 6 τ

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