Question

A certain object has a mass m $ 100 kg and is acted on by a force f (t) = 500[2 – e^-t sin(5πt)] N. The mass is at rest at t = 0. Use MuPAD to compute the object’s velocity at t = 5 s. The equation of motion is mυ̇ = f(t).

Answer 1

 

The force acting on the object is given. It is required to find the velocity after 5 seconds. The equation given in the question is:

mv̇ = f(t)

 

The above equation can be integrated to find the value of the velocity

v = ∫⁵₀ f(t)/m

f(t) = 500[2 – e^-t sin(5πt)]

m = 100

 

This can be achieved in MATLAB using the command int(f, a, b) where f is the function and a and b are the limits.

 

The MATLAB code is given below.

Input:

syms t

f = 500*(2-exp(-t)*sin(5*pi*t));

m = 100;

v = int(f/m, 0, 5)

 

Output:

 

We see that velocity is 49.68.

 

We see that velocity is 49.68.