What is the maximum acceleration when phase angle is given
Shiva , 4 Years ago
Grade 12
Mechanics> What is the maximum acceleration when pha...
3 Answers
Arun
Last Activity: 4 Years ago
a
max
=Aω
2
.....(1)
V
max
=Aω
Now,
V
max
a
max
=
Aω
Aω
2
=ω
i.e =ω=10
o
displacement =A
m
cos(ωt+θ)
=Acos(0+
4
1
)
=Acos
4
1
5=A
2
1
⇒A=5
2
Now a
max
=5
2
×10
2
from (1)
=10×5
2
=500
2
m/s
2
Vikas TU
Last Activity: 4 Years ago
Dear student
Above ans is not understandable
Phase difference between acceleration and velocity in SHM is 90 degrees.
Let's see by practical example instead of trigonometry.
Case of swinging pendulum. When it's at mean position , acceleration is 0 because no restoring force acts on it. However velocity is maximum here. Now when pendulum reaches right extremity it's velocity becomes 0 at the moment of reversal, but here acceleration becomes maximum!
Now again when pendulum reaches mean position from right side it's velocity becomes maximum. But now again acceleration becomes 0.
This is quarter part of oscillation from mean to one extremity. Or from extremity to mean.
To arrive at maximum acceleration from maximum velocity pendulum has to travel 1/4 th part of oscillation means quarter part of 360 degrees. It's 90 degrees or Pi ÷2 radian. Same for its travel from minimum (0) acceleration to minimum (0) velocity.
This can also be proved by maths using equation of displacement in SHM taking
Displacement x=A sin wt considering travel from mean position. Differentiate for velocity and again for acceleration. You find that phase difference is 90 degrees.
Ayush_Deep
Last Activity: 4 Years ago
Don't be so much confused due to irritable answers .
max. Acceleration = AW²
Max. Velocity = AW
Their ratio as given will be W = 10 s-¹
Now the equation of SHM will be
, x= Asin(Wt + π/4)
At t=0 , x= 5 so, amplitude will 5/sin(π/4)
A=5√2
Max. Acceleration = AW²= 5√2 * 10²
= 500√2
Good regards thanks
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on Mechanics
A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mmat the free end, where a small mass of 2 g is positioned. determine(i) The velocity of the end when passing through the zero position(ii) The acceleration at maximum displacement(iii) The maximum kinetic energy of the mass
Mechanics
2 Answer Available
Last Activity: 2 Year ago(s)
An object of mass m = 0.25 kg oscillates in a fluid at the end of a vertical spring of springconstant kH = 85 N/m, see Fig.1. The effect of the fluid resistance is governed by thedamping constant b = 0.07kg/s.(i) Find the period of the damped oscillation.(ii) By what percentage does the amplitude of the oscillation decrease in each cycle?
Mechanics
1 Answer Available
Last Activity: 2 Year ago(s)
If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0
Mechanics
1 Answer Available
Last Activity: 2 Year ago(s)
A particle is traveling in a circle of radius R =2.5m and with an angular velocity of 10 rad/s. What is the centripetal acceleration of the particle? The particle begins to slow down with an angular acceleration of -1 rad/s2. After 5 seconds, what is the centripetal acceleration and the tangential acceleration fo the particle?
Mechanics
1 Answer Available
Last Activity: 2 Year ago(s)
If the acceleration of block A is 5 m/s^2Find the acceleration of block B
Mechanics
1 Answer Available
Last Activity: 2 Year ago(s)