1.

A cart of mass `2.00kg` is attached to the end of a horizontal spring with force constant `k = 150N//m`. The cart is displaced `15.0cm` from its equilibrium position and released. What are (a) the amplitude (b) the period ( c) the mechanical energy (e) the maximum velocity of the cart ? Neglect friction.

Answer» Correct Answer - A::B::C::D
(a) A = initial displacement from mean position
`= 15cm`
(b) `T = 2pi sqrt((m)/(k)) = 2pi sqrt ((2.0)/(150)) = 0.726 s`
( c) `F = (1)/(T) = 1.38Hz`
(d) `E = (1)/(2)kA^(2)`
`= (1)/(2) xx 150 xx (0.15)^(2) = 1.69 J`
(e) `v_(max) = omega A`
`= ((2pi)/(T)) A = ((2pi)/(0.726))(0.15)`
` = 1.30 m//s`


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