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The displacement of a 500 g mass, undergoing simple harmonic motion, is defined by the function :

Delicious77 [7]

The maximum kinetic energy, maximum potential energy and the maximum mechanical energy are equal to 7.56J.

<h3>What is simple harmonic motion?</h3>

Simple harmonic motion, in physics, repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side.

Simple Harmonic Motion

The given equation of the simple harmonic motion is

$x=3.5 sin (\frac{\pi }{2t} + \frac{5\pi }{4} )$

Data;

ω = π/2

k = 1.254N/m

Solving this

$\frac{dx}{dt} = -3.5 X \frac{\pi }{2} cos (\frac{x\pi t}{2}+\frac{5\pi }{4} )$

Let's calculate the maximum velocity.

$V_{m} =\frac{3.5\pi }{2}$

This is only possible when cos θ = -1

The maximum kinetic energy is

$K_m =\frac{1}{2} mv^2 = \frac{1}{2} X \frac{500}{1000} X \frac{7^2\pi ^2}^{4} ^2$

$w^2 = \frac{k}{m} \\k = w^2m\\k = \frac{\pi ^2}{4} X \frac{500}{1000} \\k =1.254 N/m$

Using the value of spring constant, we can find the maximum potential energy.

$P.E =\frac{1}{2} k x^2\\P.E =\frac{1}{2} X 1.234 X 3.5^2 \\P.E = 7.56 J$

The maximum potential energy is 7.56J

The maximum mechanical energy is equal to the sum of maximum potential energy and the maximum kinetic energy.

ME = K.E + P.E

ME = 7.56J

From the calculations above, the maximum kinetic energy, maximum potential energy and the maximum mechanical energy are equal to 7.56J.

Learn more on simple harmonic motion here;

brainly.com/question/15556430

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8 0

2 years ago

what is the average gravitational force of attraction between the earth and the sun? the earth averages a distance of about 150

Tanzania [10]

Answer:

B

Explanation:

Hhhhh

5 0

3 years ago

QUESTION 1

Sveta_85 [38]

distance from the Sun of 2.77 astronomical units or about 414 million km 257 million miles and orbiting period of 4.62 years

7 0

3 years ago

A constant power is supplied to a rotating disc .the relationship of angular velocity of disc and number of rotations made by th

Bogdan [553]

A rotating disc supplied with constant power where the relationship of the angular velocity of the disc and the number of rotations made by the disc is governed by Newton's second law for rotation. This law is specially made for rotating bodies which is extracted from Newton's second law of motion.

6 0

3 years ago

What is the best description of the end result of chemical bonding for most

forsale [732]

A. Getting a full set of valence electrons

Explanation:

The best description of the end result of chemical bonding for most atoms is the getting of a full set of valence electrons.

Atoms reacts with one another in order to complete valence electronic shell.

The valence electron shell is the outermost energy level of an atom.
It is from this energy level that electrons are lost or gained to form bonds.
All atoms wants to be like the noble gases whose valence electronic shell is completely filled up
This is the crux of chemical bonding
The attraction that is produced from the interaction leads to bond formation

learn more:

Chemical bond brainly.com/question/10903097

#learnwithBrainly

7 0

3 years ago