The maximum speed of the object under simple harmonic motion is 0.786 m/s.
The given parameters:
- Position of the particle, y = 0.5m sin(πt/2)
<h3>Wave equation for
simple harmonic motion;</h3>
y = A sin(ωt + Ф)
where;
- A is the amplitude = 0.5 m
- ω is the angular speed = π/2
The maximum speed of the object is calculated as follows;

Thus, the maximum speed of the object under simple harmonic motion is 0.786 m/s.
Learn more about simple harmonic motion here: brainly.com/question/17315536
Answer:

Explanation:
When a standing wave is formed with six loops means the normal mode of the wave is n=6, the frequency of the normal mode is given by the expression:

Where
is the length of the string and
the velocity of propagation. Use this expression to find the value of
.

The velocity of propagation is given by the expression:

Where
is the desirable variable of the problem, the linear mass density, and
is the tension of the cord. The tension is equal to the weight of the mass hanging from the cord:

With the value of the tension and the velocity you can find the mass density:


Hello!
First one we can use that PE=mgh so we have
4.37*10^5J/(9.12*10^3kg*9.80m/s^2)= 4.89m
Second one we can use Newton’s Second Law
F=ma and in this case F=mg so we have
g= 3.28*10^-2N/6*10^-3kg = 5.47m/s^2
Hope this helps. Any questions please ask. Thank you.
Part a)
At t = 0 the position of the object is given as

At t = 2

so displacement of the object is given as

so average speed is given as

Part b)
instantaneous speed is given by


now at t= 0

at t = 1


at t = 2

Part c)
Average acceleration is given as



Part d)
Now for instantaneous acceleration
As we know that

at t = 0

at t = 1

now we have

At t = 2 we have



<em>so above is the instantaneous accelerations</em>