Question

Calculate Using Maltab.

The displacement of the oscillating spring can be described by:
x = A*cos(ω*t)
where:
x = displacement at time t, +ve means upward -ve means downwards
A = maximum displacement,
ω = angular frequency in radians per second, and
t = time in seconds

If the maximum displacement A = 4 cm and the angular frequency is 0.6 radians per second.
What is the shortest time at which the displacement is equal to 2 cm (upwards)?

a)1.745

b) 1.111

c) 3.492

d) 6.984

*Explain the steps and process and how you calculated the correct answer.

Answer 1

ANSWER OPTION A

x = Acos(wt)

x/A = cos(wt)

wt = cos^-1(x/a)

put values,

wt = cos^-1(0.5)

wt = pi/3

t = pi/(3*w)

t = 1.745s ANS

MATLAB CODE:

x = 2;
A = 4;

w = 0.6;

%acos function to find cos inverse, using formula of t
t = acos(x/A)/w;

CODE SNIPPET:

WORKSPACE OUTPUT:

As we can see, t = 1.745 s.

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