y(t) = distance of weight from equilibrium position

ω= angular frequency (measured in radians per second)

A = amplitude

Ø= phase (depends on initial conditions)

c1 = A sin

c2 = A cos

Prove that: Asin(ωt+Ø)=c2sinωt+c1cosωt

Note: c1 and c2 are actually with the number slightly below the letter, if that makes sense. It wouldn't let me type it that way. Anyway, if anyone can help I would really appreciate it! Thank you!

An object moving along the x-axis is said to exhibit simple harmonic motion if its position as a function of time varies as

x(t) = x0 + A cos(ωt + φ).

The object oscillates about the equilibrium position x0.  If we choose the origin of our coordinate system such that x0 = 0, then the displacement x from the equilibrium position as a function of time is given by

x(t) = A cos(ωt + φ).

A is the amplitude of the oscillation, i.e. the maximum displacement of the object from equilibrium, either in the positive or negative x-direction.  Simple harmonic motion is repetitive.  The period T is the time it takes the object to complete one oscillation and return to the starting position.  The angular frequency ω is given by ω = 2π/T.  The angular frequency is measured in radians per second.  The inverse of the period is the frequency f = 1/T.  The frequency f = 1/T = ω/2π of the motion gives the number of complete oscillations per unit time.  It is measured in units of Hertz, (1 Hz = 1/s).

The velocity of the object as a function of time is given by

v(t) = dx(t)/dt = -ω A sin(ωt + φ),

and the acceleration is given by

a(t) = dv(t)/dt = -ω2A cos(ωt + φ) = -ω2x.

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.

it would take 5 hours i think idk i'm not that good at math.can you me with my questions i need asap.