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Answer:
Explanation:
a )
Amplitude A = 14 mm , angular frequency ω = 2π / T
= 2π / .5
ω = 4π rad /s
φ₀ = initial phase
Putting the given values in the equation
14 = 25 cos(ωt + φ₀ )
14/25 = cosφ₀
φ₀ = 56 degree
x(t) = 25cos(4πt + 56° )
b )
maximum velocity = ω A
= 4π x 25
100 x 3.14 mm /s
= 314 mm /s
At x = 0 ( equilibrium position or middle point , this velocity is achieved. )
maximun acceleration = ω² A
= 16π² x A
= 16 x 3.14² x 25
= 3943.84 mm / s²
3.9 m / s²
It occurs at x = A or at extreme position.
