Question

he equation of motion of a simple harmonic oscillator is given by x(t) = (7.4 cm)cos(12πt) − (4.2 cm)sin(12πt), where t is in seconds.Find the amplitude. m (b) Determine the period. s (c) Determine the initial phase. °

Answer #1

Initial phase = 2.087 radian = 2.087×180/π = 119.58°

The position of an object in simple harmonic motion is given by
x= (6.88 cm) cos [(2 pie/0.663 s)t]
(a) What is the object's speed at 0.828 s?
cm/s
(b) What is the object's maximum speed?
cm/s
(c) What is the object's speed when -6.88 cm?
cm/s

The function x = (8.0 m) cos[(4πrad/s)t + π/5 rad] gives the
simple harmonic motion of a body. At t = 6.9 s, what are the (a)
displacement, (b) velocity, (c) acceleration, and (d) phase of the
motion? Also, what are the (e) frequency and (f) period of the
motion?

The function x = (9.5 m) cos[(6πrad/s)t + π/4 rad] gives the
simple harmonic motion of a body. At t = 2.3 s, what are the (a)
displacement, (b) velocity, (c) acceleration, and (d) phase of the
motion? Also, what are the (e) frequency and (f) period of the
motion?

The function x = (6.4 m) cos[(4πrad/s)t + π/3 rad] gives the
simple harmonic motion of a body. At t = 3.2 s, what are the (a)
displacement, (b) velocity, (c) acceleration, and (d) phase of the
motion? Also, what are the (e) frequency and (f) period of the
motion?

In an engine, a piston oscillates with simple harmonic motion so
that its position varies according to the expression, x = 7.00
cos(3t + π/7) where x is in centimeters and t is in seconds.
(a) At t = 0, find the position of the piston. ____ cm
(b) At t = 0, find velocity of the piston. ____ cm/s
(c) At t = 0, find acceleration of the piston. ____ cm/s^2
(d) Find the period and amplitude of the...

An object undergoes simple harmonic motion along the x-axis with
a period of 0.5 s and an amplitude of 25 mm. Its position is x = 14
mm when t = 0 and it is heading in the -x-direction (negative). In
your logbook write an equation of motion with all the variables
identified and sketch a graph of position vs. time for the
oscillator. What is the initial phase? [Work in rotational
coordinates to 2 s.f. and enter nothing at...

In an engine, a piston oscillates with simple harmonic motion so
that its position varies according to the expression,
x = 8.00 cos (3t + pi/4)
where x is in centimeters and t is in
seconds.
(a) At t = 0, find the position of the piston.
cm
(b) At t = 0, find velocity of the piston.
cm/s
(c) At t = 0, find acceleration of the piston.
cm/s2
(d) Find the period and amplitude of the motion.
period...

1)x = (9.2 m) cos[(5πrad/s)t + π/4
rad]
gives the simple harmonic motion of a body. At t = 2.1 s,
what are the (a) displacement,
(b) velocity, (c) acceleration,
and (d) phase of the motion? Also, what are the
(e) frequency and (f) period of
the motion?
2) An oscillating block-spring system takes 0.746 s to begin
repeating its motion. Find (a) the period,
(b) the frequency in hertz, and
(c) the angular frequency in radians per
second.

3. Consider the nonlinear oscillator equation for x(t) given by
?13 ?
x ̈+ε 3x ̇ −x ̇ +x=0, x(0)=0, x ̇(0)=2a
where a is a positive constant. If ε = 0 this is a simple
harmonic oscillator with frequency 1. With non-zero ε this
oscillator has a limit cycle, a sort of nonlinear center toward
which all trajectories evolve: if you start with a small amplitude,
it grows; if you start with a large amplitude, it decays.
For ε...

A simple harmonic oscillator has a frequency of 11.1 Hz. It is
oscillating along x, where x(t) = A cos(ωt + δ). You are given the
velocity at two moments: v(t=0) = 1.9 cm/s and v(t=.1) = -18.1
cm/s.
1) Calculate A.
2) Calculate δ.

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