# Solve the following LaPlace transform questions. Derive the Laplace transform of the ramp function..

Solve the following LaPlace transform questions. Derive the Laplace transform of the ramp function f(t) = tu(t) where u(t) is the unit step function. Obtain a solution to the following first order ODE for the given initial condition using Laplace transforms v(t) + 1 / tau v(t) = 0, v(0) = 1, where tau is a constant (known as the “time constant”). The spring-mass mechanical system is initially at rest. The displacement .x(t) of mass m is measured from the neutral position. At t = 0, mass m is set into motion by a unit impulse force f(t) = delta(t). Write the equation of motion and obtain the

Solve the following LaPlace transform questions. Derive the Laplace transform of the ramp function f(t) = tu(t) where u(t) is the unit step function. Obtain a solution to the following first order ODE for the given initial condition using Laplace transforms v(t) + 1 / tau v(t) = 0, v(0) = 1, where tau is a constant (known as the “time constant”). The spring-mass mechanical system is initially at rest. The displacement .x(t) of mass m is measured from the neutral position. At t = 0, mass m is set into motion by a unit impulse force f(t) = delta(t). Write the equation of motion and obtain the solution for the displacement .x(t) using Laplace transform. Obtain the inverse Laplace transform of the following function using partial fraction expansion X(s) = 3s + 6 / s3 + 3s2 + 2s

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