Solving Equation of Motion for A and \Phi

[krnhseya]

Homework Statement

A sin (wt + $$\Phi$$) = 0
Find A and $$\Phi$$

Homework Equations

Asin(wt)cos$$\Phi$$ + Acos(wt)sin$$\Phi$$ = 0

The Attempt at a Solution

I was told to use magnitude to figure out A and something else to find $$\Phi$$ in variable.
I absolutely have no idea what to do...
I found a part of solution, which got me w and I am expected to solve for A and $$\Phi$$ with that given equation.

I tried to use original equation by plugging in t = 0 for A sin (wt + $$\Phi$$) and first and second derivative from original equation.

I think once I get those A and $$\Phi$$, I "might" be able to solve entire problem.

Thank you.

 

[krnhseya]

is there missing info or ?

 

[Moetasim]

I would first suggest reviewing the basic principles of trigonometry and how it relates to solving equations. From the given equation, we can see that it is in the form of a sine function, which can be represented as a right triangle. The amplitude A is the hypotenuse of this triangle, while \Phi is the angle between the hypotenuse and the x-axis.

To solve for A, we can use the Pythagorean theorem to find the magnitude of A. This can be done by squaring both sides of the equation and then taking the square root of both sides. This will give us the value of A.

To solve for \Phi, we can use the inverse trigonometric functions, specifically the arccosine function. This function will give us the angle \Phi when given the ratio of the adjacent and hypotenuse sides of the triangle. In this case, we can use the values of A and w to find this ratio and then use the arccosine function to solve for \Phi.

I would also suggest checking your solution by plugging in the values of A and \Phi into the original equation and making sure it satisfies the equation. Additionally, it may be helpful to graph the equation to visualize the solution and make sure it makes sense in the context of the problem.

Overall, solving equations involving trigonometric functions requires a solid understanding of trigonometry and its properties. I would recommend reviewing these concepts and practicing solving similar equations to gain a better understanding of the process.