A particle moves along the x-axis according to the law If the particle is started at x = 0 with an initial velocity of 12 ft/s to the left, determine x in terms of t.

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Question

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BPSC Assistant Professor Mechanical 2022 Official Paper

Answer 1

Concept:

Laplace transform:

L [Sin at] =

Calculation:

Given:

................................. (1)

At t = 0, x = 0; , at t = 0

i.e. x (0) = 0, x' (0) = -12 are the initial conditions

Now, taking laplace transform on both sides of (1)

∴ L [x'' (t)] + 6 × L [x' (t)] + 25 × L [x (t)] = L (0)

⇒ { } + 6 × {} + 25 × L [x (t)] = 0

Using initial conditions:

= -12

⇒ L [x (t)] =

⇒ x (t) =