Question

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 motion.

period = ____ s

amplitude = ____ cm

Answer #1

Given expression is -

x(t) = 7.00 cos(3t + π/7)

Differentiate this with respect to t -

x'(t) = v(t) = -21.0 sin(3t + π/7)

Again differentiate -

x''(t) = a(t) = -63.0cos(3t + π/7)

where you need to differentiate using the chain rule

(a) At t = 0, position = x(0) = 7.0 cos(π/7) = 6.31 cm

(b) At t = 0, velocity = v(0) = -21.0 sin(π/7) = -9.11 cm/s

(c) At t = 0, acceleration = a(0) = -63.0 cos(π/7) = -56.76 cm/s²

Now, comparing 7.0cos(3t + π/7) with Acos(wt + φ)

where A is the amplitude, w = 2π/T is the angular frequency, T is
the period, and φ is the phase shift

you get

(d) Period (T) -

w = 2π/T = 3.0

=> T = 2π/3.0 = 2.09 s

(e) Amplitude, A = 7.0 cm

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...

Answer both sections:
A) The motion of a piston in an auto engine is simple harmonic.
If the piston travels back and forth over a total distance of 12
cm, and the piston has a mass of 1.8 kg, what is the maximum force
acting on the piston when the engine is running at 4,800 rpm
(revolutions per minute)? Round your answer to the nearest Newton.
Enter the numerical answer only with no units.
B)
A body oscillates with simple...

A mass oscillates on a horizontal spring in a simple harmonic
motion. It is observed that the duration of one full oscillation
cycle is 0.50 π seconds, and that the maximal displacement of the
oscillator from the equilibrium is 12.0 cm. Let time instant taken
as t = 0.00 sec correspond to the moment when the mass is at the
location 10.0 cm to the left of the equilibrium, and moving to the
left.
1. Find oscillator’s velocity and acceleration...

For an object with simple harmonic motion;
a) What can you say about its speed, acceleration and kinetic
energy at equilibrium?
b) For simple harmonic motion given by x = 3,8 cos (5πt / 4 + π / 6), what is its amplitude, frequency, position and speed for t = 0?

A piston (with mass M = 2.0 kg) in a car engine is in vertical
simple harmonic motion with amplitude A = 5.0 cm. If the engine is
running at 3556 rev/min,
(a) What is the maximum velocity (m/s) of the piston?
(b) What is the maximum acceleration (m/s2) of the piston?
Suppose a small 100 g piece of metal were to break loose from the
surface of the piston
when it (the piston) is at the lowest point (z...

A particle moving along the x axis in simple harmonic motion
starts from its equilibrium position, the maximum value, at t = 0,
moving to the right. The amplitude of the motion is 2.00 cm and the
frequency is 1.50 Hz. (a) Find an expression for the position of
the particle as a function of time. Determine (b) the maximum speed
of the particle and (c) the earliest time (t > 0) at which the
particle has this speed. Find...

A mass of 100 g is attached to a spring and oscillating with
simple harmonic motion. The position of the mass at all times is
given by
x(t) = (2.0 cm) cos(2t),
where t is in seconds, and the 2 is in rad/s. Determine
the following:
(a) The amplitude (in cm).
cm
(b) The frequency.
Hz
(c) The maximum speed in cm/s. Think about the
expression you can write for v(t). Where is the
maximum velocity in that expression? You...

Model a piston in an engine as a mass on a spring that is
undergoing simple harmonic motion. The mass of the piston is 0.583
kg, and the period of the motion is 1.54 seconds. The motion has an
amplitude of 0.0902 meters, meaning the distance between the center
of the motion and each end of the motion. Assume that the mass
starts out with the spring stretched as far as it is going to go,
so that the phase...

The position of an object in simple harmonic motion as a
function of time is given by ? = 3.8??? (5??/4 + ?/6) where t is in
seconds and x in meters. In t = 2.0s calculate (a) the period, (b)
the oscillation frequency (c) velocity and (d) acceleration.

The motion of a piston in an automobile engine is nearly simple
harmonic. If the 1-kg piston travels back and forth over a total
distance of 14.8 cm, what is its maximum speed, in m/s, when the
engine is running at 3,504 rpm? Give your answer in m/s and use
only one decimal place (just one digit after decimal point).

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 5 minutes ago

asked 28 minutes ago

asked 40 minutes ago

asked 47 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago