Mechanical and Materials Engineering Homework Solutions

If the complex numbers z = x+jy and w = u+jv

If the complex numbers z = x+jy and w = u+jv are said to be equal, then: a. z = w b. u = x c. v = y d. All of the above

Linear or non differential equation

Please see attached file for equation a. Linear, time-invariant b. Linear, constant-coefficient c. None linear, time-variant d. Both a and b

Laplace transform of unit impulse

See attached file for full problem description.

Laplace transform of a sine function

Laplace transform of a sine function. See attached file for full problem description.

Inverse Laplace Transform

Inverse Laplace Transform. See attached file for full problem description.

A ball with a mass of 0.25 kg is thrown vertically upward

A ball with a mass of 0.25 kg is thrown vertically upward with an initial velocity of 10 m/s. What is the velocity of the ball when it reaches the highest point? a. 10 m/s b. 0.25 m/s c. 0 m/s d. Can not be determined How many seconds would it take for the ball to reach its maximum height. a. 10s b. 1.02 s c. 0.25 s d ...continues

Kinetic energy and force of a car

A car of mass 1500 kg is moving with a speed of 50 km/h (13.89 m/s). Determine the kinetic energy T of the car. (see options a through d in attached file) Now determine the force required to stop the car at a distance of 50 m, if the kinetic energy T is 1.447 x 10E5 N-m. 10E5 means 10 to the 5th power. a. 1447 N b. 289 ...continues

Braking of a car/deceleration/distance

A brake is applied to a car traveling at a constant speed of 25 m/s. If the deceleration caused by the braking action is 5 m/per second squared, find the time before the car stops. a. 1s b. 2s c. 4s d. 5s Determine the distance traveled before the car stops, IF the car stops at t = 5 seconds. a. 52.5 m b. 62.5 m c. 25 ...continues

Capacitance of a pressure vessel

(See attached file for full problem description)

Error of linearized equation

(See attached file for full problem description)

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