Question

A machine part is undergoing Simple Harmonic Motion with a frequency of 5.10 Hz and amplitude 1.80 cm.

(a) Determine the angular velocity “ω” of the oscillation.

(b) What is the displacement
of this oscillation at t=5 sec if it follows the part of x=A cos
(ωt) with *x*=0 m at equilibrium?

Answer #1

(1) frequency and amplitude of SHM is given as;

solution:

(A) Angular velocity can be defined as;

(B) displacement of this oscillation is given as;

at t = 5 s;

A) A mass on a spring vibrates in simple harmonic motion at a
frequency of 4.0 Hz and an amplitude of 8.0 cm. If a timer is
started when its displacement from equilibrium is a maximum (hence
x = 8 cm when t = 0), what is the displacement of the mass when t =
3.7 s?
B) A mass of 4.0 kg, resting on a horizontal, frictionless
surface, is attached on the right to a horizontal spring with
spring...

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.

A metal ball attached to a spring moves in simple harmonic
motion. The amplitude of the ball's motion is 11.0 cm, and the
spring constant is 5.50 N/m. When the ball is halfway between its
equilibrium position and its maximum displacement from equilibrium,
its speed is 27.2 cm/s.
(a) What is the mass of the ball (in kg)?
(b) What is the period of oscillation (in s)?
(c) What is the maximum acceleration of the ball? (Enter the
magnitude in...

A diving board oscillates with simple harmonic motion of
frequency 3.85 Hz.
What is the maximum amplitude with which the end of the board can
vibrate in order that a pebble placed there not lose contact with
the board during the oscillation?

A plastic ball attached to a spring moves in simple harmonic
motion. The amplitude of the ball's motion is 11.5 cm, and the
spring constant is 6.00 N/m. When the ball is halfway between its
equilibrium position and its maximum displacement from equilibrium,
its speed is 22.7 cm/s.
What is the mass of the ball (in kg)?
Answer- kg
What is the period of oscillation (in s)?
Answer- s
What is the maximum acceleration of the ball? (Enter the...

An object undergoing simple harmonic motion takes 0.23 s to
travel from one point of zero velocity to the next such point. The
distance between those points is 33 cm. Calculate
(a) the period, (b) the
frequency, and (c) the amplitude of the
motion.

A mass at the end of a horizontal ideal spring undergoes simple
harmonic motion of amplitude 0.700 m and of frequency 3.00 Hz as it
slides on a frictionless horizontal surface. The particle is at x =
0.700 m at time t = 0.00 s. The magnitude of the force on the
particle at t = 0.00 s is 14.6 N.
Calculate:
(a) the position of the particle at t = 0.452 s,
(b) the velocity of the particle at...

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...

The speed of a particle undergoing simple harmonic motion is
suddenly doubled when the particle's displacement is one-half the
amplitude. What is the new amplitude?
Book: A First Course in Analytical Mechanics by Klaus
Rossberg

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.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 16 minutes ago

asked 28 minutes ago

asked 56 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago