If the equation of motion of a particle is given by s = A cos(ωt + δ),
the particle is said to undergo simple harmonic motion. s'(t) = Aω sin(ωt + δ)
When is the velocity 0? (Use n as the arbitrary integer.)
t= _____________
I thought it was 0, but it said it was wrong.
 👍
 👎
 👁
 ℹ️
 🚩
1 answer

The solution to t in the following equation is the right answer.
s'(t) = Aω sin(ωt + δ) = 0
Since it is an SHM (simple harmonic motion), there are many solutions.
Think of riding on a swing. When you reach the highest point, the velocity is zero. But every time you ride to the top (on each side of the swing), the velocity is zero. So this happens every 2 seconds or so. The arbitrary integer n is used to denote the sequence.
Back to the equation:
s'(t) = Aω sin(ωt + δ) = 0
Since we know the amplitude A is not zero, and the frequency ω is not zero, so sin(ωt + δ)=0
The solution of
sin(ωt + δ)=0
is
ωt + δ)= nπ
(see link at end of post)
So solve for t to get:
t=(nπδ)/ω
http://www.google.ca/imgres?imgurl=http://intmstat.com/trigonometricgraphs/sinx.gif&imgrefurl=http://www.intmath.com/trigonometricgraphs/1graphssinecosineamplitude.php&h=207&w=328&sz=3&tbnid=oJ2eIaeurAqkM:&tbnh=84&tbnw=133&prev=/search%3Fq%3Dsine%2Bcurve%26tbm%3Disch%26tbo%3Du&zoom=1&q=sine+curve&docid=UDPUCTbk1CVnM&hl=en&sa=X&ei=aY3VTofDJsXn0QGnv9yGAg&sqi=2&ved=0CDQQ9QEwAQ&dur=3321 👍
 👎
 ℹ️
 🚩
answered by MathMate
Answer this Question
Related Questions

Physics HELP
1.If a particle moves in a plane so that its position is described by the functions x=A*cos(wT) and y=A*sin(wT), the particle is ( wangular velocity, Tperiod) A) moving with constant speed along a circle B) moving with a varying speed along a circle
 asked by Kelly
 2,017 views

physics
A particle moves in a circle in such a way that the x and ycoordinates of its motion are given in meters as functions of time t in seconds by: x=5cos(3t) y=5sin(3t) What is the period of revolution of the particle? Here's what my train of thought was...
 asked by Hannah
 3,871 views

Calculus
A particle moves along a line so that at any time t its position is given by x(t)=2(pi)t+cos(2(pi)t). Determine the particle's maximum velocity.
 asked by MEG
 4,789 views

CALCULUS PLEASE HELP!!!
SHOW WORK PLEASE!!! The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin πt + 3 cos πt, where t is measured in seconds. (Round your answers to two decimal places.) (a)
 asked by TENSHI
 15,978 views

math
The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 6/t2, where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3.
 asked by Yuxiang Nie
 971 views

calculus
The position of a particle moving in a straight line is given by s(t) = (e^(t))(cos(5t)) for t>0, where t is in seconds. If the particle changes direction at time T seconds, then T must satisfy the equation: a. tan(5T) = 4.8 b. cos(5T) = 0 c. e^(T) =
 asked by lovejoy
 1,113 views

science
the velocity of a particle is given by v=[16t^2i+4t^3j +(5t+2)k]m/s, where t is in seconds. If the particle is at the origin when t=0, determine the magnitude of the particle's acceleration when t=2s. What is the x,y,z coordinate position of the particle
 asked by sarah
 3,533 views

physics
The motion of a human body through space can be modeled as the motion of a particle at the body's center of mass. The components of the position of an athlete's center of mass from the beginning to the end of a certain jump are described by the following
 asked by Spice
 1,737 views

math
Let s ( t ) = 4 t 3 + 48 t 2 + 180 t be the equation of motion for a particle. Find a function for the velocity. v ( t ) = Where does the velocity equal zero? [Hint: factor out the GCF.] t= and t= Find a function for the acceleration of the particle. a(t)=
 asked by Juan
 1,015 views

physics
A 1.6 kg particle moving along the xaxis experiences the force shown in the figure. The particle's velocity is 4.2 m/s at x = 0 m. The figure or graph has F (N) along the y axis and velocity along the x axis. A diagonal line drops from positive 10 force
 asked by Hope
 4,954 views

conceptual physics problem
A particle is oscillating in simple harmonic motion. The time required for the particle to travel through one complete cycle is equal to the period of the motion, no matter what the amplitude is. But how can this be, since larger amplitudes mean that the
 asked by Miss.Seena
 1,001 views

Calculus
Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = cos^2 t, y = cos t, 0 ≤ t ≤ 9π and the length of the curve so far i got ∫0 to 9pi √((2cos(t)sin(t))^2+(sint)^2) I am having trouble
 asked by rob
 1,540 views

selfstudy calculus
Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. r(t)=cos(t)I cos(t)j+sin(t)k I don't know what to do. I let x=cos(t), y=cos(t) and z= sin(t). Should I let t be any number and get the equal
 asked by Anonymous
 1,735 views

physics
A stone is thrown vertically upwards with a velocity 30 ms −1 . If the acceleration due to gravity is 10 ms −2 , what is the distance travelled by the particle during the first second of its motion?
 asked by Anonymous
 521 views

Physics
Starting from rest a particle confined to move along a straight line is accelerated at a rate of 5m/s. Describe the motion of the particle.
 asked by Joe
 1,696 views

Calculus
The velocity of a particle moving along the xaxis at any time t >= 0 is given by v(t) = cos(pi t)  t(7  2pi). a. Find the acceleration at any time t. b Find the particle's maximum acceleration over the interval [0, 2]. Use derivatives to support and
 asked by Sarah
 972 views

Diff eqn IVP
A simple pendulum of length is oscillating through a small angle θ in a medium for which the resistance is proportional to the velocity. Obtain the differential equation of its motion and discuss the motion.
 asked by shasha
 1,469 views

Physics
A particle has a charge of +1.5 µC and moves from point A to point B, a distance of 0.18 m. The particle experiences a constant electric force, and its motion is along the line of action of the force. The difference between the particle's electric
 asked by ali
 4,865 views

Calculus 1
A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and speed when t = 5. (Round your answers to two decimal places.) f(t) = t^−1 − t *We havent learned derivative
 asked by TayB
 7,818 views

Calculus
The equation of motion of a particle is s = t3 − 12t, where s is in meters and t is in seconds. For the velocity function, I got v(t)=3t^212 and for acceleration, a(t)=6t. The final question is: Find the acceleration when the velocity is 0. How do I do
 asked by Kelly
 7,980 views
Still need help?
You can ask a new question or browse existing questions.