A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 3.40 cm, and the frequency is 1.70 Hz. a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t. Assume that x is in centimeters and t is in seconds. Do not include units in your answer.) b) Determine the maximum speed of the particle. c) Determine the earliest time (t > 0) at which the particle has this speed
A particle moving along the x axis in
a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t. Assume that x is in centimeters and t is in seconds. Do not include units in your answer.)
b) Determine the maximum speed of the particle.
c) Determine the earliest time (t > 0) at which the particle has this speed
d) Find the maximum positive acceleration of the particle.
e) Find the earliest time (t > 0) at which the particle has this acceleration.
f) Determine the total distance traveled between t = 0 and t = 0.88 s.
 alt="A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 3.40 cm, and the frequency
is 1.70 Hz.
(a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t. Assume that x is in centimeters and t is in seconds. Do not include units in your
answer.)
3.4 sin (3.4rt)
X =
(b) Determine the maximum speed of the particle.
36.3168
cm/s
(c) Determine the earliest time (t > 0) at which the particle has this speed
.2941118
(d) Find the maximum positive acceleration of the particle.
.2
387.915
cm/s?
(e) Find the earliest time (t > 0) at which the particle has this acceleration.
.441176
S
(f) Determine the total distance traveled between t
= 0 and t = 0.88 s.
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