A particle oscillates with simple harmonic motion, so that its displacement varies according to the expression x = (5 cm)cos(2t + π/6) where x is in centimeters and t is in seconds. At t = 0 find (a) the displacement of the particle, (b) its velocity, and (c) its acceleration. (d) Find the period and amplitude of the motion. Solution:

2018年9月15日 · 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).

2011年10月11日 · 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)

2021年1月14日 · The general solutions to harmonic motion is either $$x(t)=A\sin(\omega t+\phi)$$ or $$x(t)=A\cos(\omega t+\phi)$$ or even $$x(t)=A\cos\omega t+B\sin\omega t$$ They are all equivalent they just give different values of $\phi, A$ or $B$. Pick the one you like most.

x = asin wt. If the particle is at P or Q when t = 0, then the following equation also holds: x = acos wt. The Simple Pendulum. A simple pendulum consists of a particle P of mass m, suspended from a fixed point by a light inextensible string of length a, as shown here:

x=Asin (wt+B); w a parameter | Differential Equations | Elimination of Arbitrary Constants. If you have questions, email me at [email protected] and I will do my best to help...

⇒ x = a sin (ωt + θ) Where a = amplitude, ω = frequency, and θ = phase of the wave. The phase of a wave is a constant that tells us what value the sin function has at t = 0. EXPLANATION: Given - Wave 1: \(x=asin(ω t +\frac{\pi}{6})\) Wave 2: \(x'=a cos ω t=a cos ( …