Consider a graphical representation (fig 15.3) of simple harmonic motion as described mathematically in equation 15.6. When the particle is at point A on the graph, what can you say about its position and velocity? a. The position and velocity are both positive. b. The position and velocity both are negative. c. The position is positive and the velocity is zero. d. The position is negative, and the velocity is zero. e. The position is positive, and the velocity is negative. f. The position is negative, and the velocity is positive.
Consider a graphical representation (fig 15.3) of simple harmonic motion as described mathematically in equation 15.6. When the particle is at point A on the graph, what can you say about its position and velocity? a. The position and velocity are both positive. b. The position and velocity both are negative. c. The position is positive and the velocity is zero. d. The position is negative, and the velocity is zero. e. The position is positive, and the velocity is negative. f. The position is negative, and the velocity is positive.
Consider a graphical representation (fig 15.3) of simple harmonic motion as described mathematically in equation 15.6. When the particle is at point A on the graph, what can you say about its position and velocity? a. The position and velocity are both positive. b. The position and velocity both are negative. c. The position is positive and the velocity is zero. d. The position is negative, and the velocity is zero. e. The position is positive, and the velocity is negative. f. The position is negative, and the velocity is positive.
Consider a graphical representation (fig 15.3) of simple harmonic motion as described mathematically in equation 15.6. When the particle is at point A on the graph, what can you say about its position and velocity?
a. The position and velocity are both positive.
b. The position and velocity both are negative.
c. The position is positive and the velocity is zero.
d. The position is negative, and the velocity is zero.
e. The position is positive, and the velocity is negative.
f. The position is negative, and the velocity is positive.
Transcribed Image Text:ultiplied by w. The trigonometric functions sine and cosine exhibit this
DI, so we can build a solution around one or both of them. The folloving
function is a sohution to the differential equation:
x(t) = A cos (st + d6)
(15.6)
A, o, and o are constants. To show explicitly that this solu ion satisfies Equa-
5, notice that
dx
d
Transcribed Image Text:Fgure 15.3 (Quick Quiz 15.2)
An x-tgraph fora particle under-
going simple harmonic motion.
A a particular time, the particle's
pesition is indicated by in the
graph.
Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.
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