Oct 8, 2014 · That comes from the "sum formula" that says that [tex]sin(x+ w)= sin(x)cos(w)+ cos(x)sin(w)[/tex]. If we are given asin(x)+ bcos(x), comparing to the previous formula, we would like to have a= cos(w) and b= sin(w). But that is not always possible, because that would require that [itex]a^2+ b^2= cos^2(w)+ sin^2(w)= 1[/itex] which is of course ...

Sep 15, 2018 · The graph will have the equation x = Asin(wt). Now I try to break this down in order to understand why this equation is true for SHM. Firstly, as I said the variation of x with t produces a sine curve, explaining why X is a function of sin(t).

Oct 18, 2009 · use x=Asin(wt) if the oscillation is starting from the equilibrium position (b/c if u look at a sin curve, it starts at a value of 0), and if it is starting at the amplitude, use x=Acos(wt). (b/c looking at a cosine curve, it starts at the amplitude)

Jun 12, 2012 · In order to be able to write A sin(x)+ B cos(x), for any A and B, as "R sin(x+ t)" we must "normalize" the coefficients: letting [itex]R= \sqrt{A^2+ B^2}[/itex] so that Asin(x)+ Bcos(x)= R((A/R)sin(x)+ (B/R)cos(x)) and then let cos(t)= A/R and sin(t)= B/R.

Dec 25, 2011 · If the object is at x = 0 when t = 0, then it's easiest to use a sine wave. If the object is at x = maximum (i.e. the amplitude) when t = 0 then it's easiest to use a cosine wave. However, as AlephZero noted, you can use either kind of wave in …

Mar 9, 2019 · The diagram shows the curve with equation y = f (x) The coordinates of the minimum point of the curve are (–2, –1) (a) Write down the coordinates of the minimum point of the curve with equation (i) y=f(x–5) (ii) y = 0.5 f ( x ) The graph of y=asin(x–b)+c (please see graph on picture) b) Find the value of a, the value of b and the value ...

Dec 18, 2015 · Deriving the equation for simple harmonic motion, x = Asinωt, graphically. Homework Equations ω = 2πf, where f = 1/T 2. The attempt at a solution Take a sine curve as the simple harmonic motion (displacement, x, on y-axis; time, t, on x-axis), then transform it. The min/max is the amplitude, so we can stretch the graph to say that x = Asin(t).

Aug 3, 2014 · I've noticed that everyone has its own preference whether to use $\arcsin x$ or $\sin^{-1} x$. Let me list the pro's and con's as I see them. $\sin^2 x$ is conventionally used for $(\sin x)^2$, suggesting $\sin^{-1} x$ would mean $\frac1{\sin x}$, which it …

May 31, 2010 · x=Acosθ 'A' is a constant radius is in the circle so if viewed from the side, the maximum distance the mass moves on either side of x=0 is A. When x=0, you get Acosθ or θ=π/2. So if you view from the top (circle), you will see the mass directly above x=0. If you view from the side (harmonic motion) you will see the mass at x=0.

Apr 12, 2010 · This is the same equation that holds for a body moving along the x-axis with uniform velocity v=k/w in the positive direction (from left to right). In case of Acos(wt+kx), the crest is at x=-w/k*t at time t, so the crest moves in the negative direction, from right to left. For a sine wave, Asin(wt-kx), a crest appears where wt-kx =pi/2.