Question

Calculate Using Maltab. The displacement of the oscillating spring can be described by: x = A*cos(ω*t)...

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.

Homework Answers

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.

Upvote if you liked the answer.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
If the object-spring system is described by x = (0.310 m) cos (1.55t), find the following....
If the object-spring system is described by x = (0.310 m) cos (1.55t), find the following. (a) the amplitude, the angular frequency, the frequency, and the period A = m ω = The angular frequency is ω in Acosωt. rad/s f = Hz T = s (b) the maximum magnitudes of the velocity and the acceleration vmax = m/s amax = m/s2 (c) the position, velocity, and acceleration when t = 0.250 s x = m v = m/s a...
1)x = (9.2 m) cos[(5πrad/s)t + π/4 rad] gives the simple harmonic motion of a body....
1)x = (9.2 m) cos[(5πrad/s)t + π/4 rad] gives the simple harmonic motion of a body. At t = 2.1 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion? 2) An oscillating block-spring system takes 0.746 s to begin repeating its motion. Find (a) the period, (b) the frequency in hertz, and (c) the angular frequency in radians per second.
The motion of a particle connected to a spring is described by x = 0.4 cos...
The motion of a particle connected to a spring is described by x = 0.4 cos (pi t) (in meter). a) What is its angular frequency and amplitude (maximum elongation) xmax? b) What is its speed and acceleration at t = 0.167s? c) At what time is the potential energy equal to the kinetic energy?
If the object-spring system is described by x = (0.340 m) cos (1.55t), find the following....
If the object-spring system is described by x = (0.340 m) cos (1.55t), find the following. (a) the amplitude, the angular frequency, the frequency, and the period A = m ω = rad/s f = Hz T = s (b) the maximum magnitudes of the velocity and the acceleration vmax = m/s amax = m/s2 (c) the position, velocity, and acceleration when t = 0.250 s x = m v = m/s a = m/s2
A wave on a string is described by the equation y(x,t)=3.0 cm*〖cos(〗⁡〖2π*(x/2.4m+t/(0.2 s)))〗 . X is...
A wave on a string is described by the equation y(x,t)=3.0 cm*〖cos(〗⁡〖2π*(x/2.4m+t/(0.2 s)))〗 . X is in meters and t is in seconds. Is the wave travelling to the right or to the left? _________ What is the wave speed? _________ What is the wave frequency? __________ What is the wavelength? ___________ At t=0.50 seconds what is the displacement of the string at x=0.20 meters. _________
A continuous sinusoidal longitudinal wave is sent along a very long coiled spring from an attached...
A continuous sinusoidal longitudinal wave is sent along a very long coiled spring from an attached oscillating source. The wave travels in the negative direction of an x axis; the source frequency is 24 Hz; at any instant the distance between successive points of maximum expansion in the spring is 20 cm; the maximum longitudinal displacement of a spring particle is 0.69 cm; and the particle at x = 0 has zero displacement at time t = 0. If the...
The trajectory of a particle moving on a straight line is x(t) = A cos ωt...
The trajectory of a particle moving on a straight line is x(t) = A cos ωt + B sin ωt. a) What are the units for the fixed numbers A, B and ω (the greek letter omega), assuming that x is measured in meters and t in seconds? b) There is a shortest non-zero time T such that x(t + T) = x(t); what is it? c) What is the velocity of the particle? d) What are the initial position...
If the object-spring system is described by x = (0.315 m) cos (1.60t), find the following....
If the object-spring system is described by x = (0.315 m) cos (1.60t), find the following. (a) the amplitude, the angular frequency, the frequency, and the period A=.315 m w=1.6 rad/s f=.25 HZ T=3.9s (b) the maximum magnitudes of the velocity and the acceleration vmax=.504 m/s amax=.8064 m/s^2 (c) the position, velocity, and acceleration when t = 0.250 s x= ? v=? a=?
A 200g mass oscillates with a displacement given by x(t)=(7.0 cm) cos[(5/s)t+2pi/9] Find the A. Angular...
A 200g mass oscillates with a displacement given by x(t)=(7.0 cm) cos[(5/s)t+2pi/9] Find the A. Angular frequency B. Frequency C.Period D.Spring constant E. Maximum speed F. maximum acceleration g. acceleratiom when the speed is equal to the maximum speed h. phase when t=2s I. displacment when t=2s J. velocity when t=2s k. acceleration when t=2s
A wave on a string is described by the equation y(x, t) = 2*cos(2 π(x/4m- t...
A wave on a string is described by the equation y(x, t) = 2*cos(2 π(x/4m- t /.1 s)) where x is in meters and t is in seconds. a. Is the wave travelling to the right or to the left? _________ b. What is the wave frequency? __________ c. What is the wavelength? ___________ d. What is the wave speed? _________ e. At t=0.50 seconds what is the displacement of the string at x=0.20 meters. _________