Maximum speed and magnitude of the acceleration of a spring?

AI Thread Summary
The discussion focuses on calculating the maximum speed and acceleration of a guitar string executing simple harmonic motion, described by the equation x(t)=Asin(wt+φ). The angular frequency is given as ω = 2.76 × 10^3 s−1 and the amplitude A is 1.60 mm. The maximum speed occurs when the displacement x is zero, while the maximum acceleration occurs at the maximum displacement A. The key equations for velocity and acceleration are provided, with clarification that the maximum value of the cosine function is one. The conversation emphasizes understanding the behavior of the trigonometric functions involved in the motion.
Howard Fox
Messages
38
Reaction score
2

Homework Statement


If a midpoint of a guitar string executes simple harmonic motion following the form x(t)=Asin(wt+φ), and its angular frequency is ω = 2.76 × 103 s−1 and A=1.60mm. What is then its maximum speed of the string during this motion? And what is the maximum magnitude of the acceleration of the spring?

Homework Equations


x(t)=Asin(wt+φ)
dx/dt = Aω cos(ωt + φ)
dv/dt = −Aω2 sin(ωt + φ)

The Attempt at a Solution


I know that the maximum velocity should happen when x=0 and the maximum acceleration is when displacement is greatest, but I am not sure on how to proceed. Should I set the second equation I listed above equal to zero to find the velocity and the third equation equal to 1.60mm to find the acceleration?
Thank you for your help.
 
Physics news on Phys.org
Howard Fox said:
Should I set the second equation I listed above equal to zero ...
No, just look at it. The right side is maximum when the cosine is maximum. What is the maximum value of a cosine, any cosine?
 
kuruman said:
No, just look at it. The right side is maximum when the cosine is maximum. What is the maximum value of a cosine, any cosine?
One?
 
What is dx/dt ?
 
Howard Fox said:
One?
One.
 
  • Like
Likes Howard Fox
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

S.H.M of the midpoint of a guitar string
Replies
3
Views
3K
Two spring-coupled masses in an electric field (one of the masses is charged)
Replies
1
Views
915
Finding amplitude from simple harmonic equation function
Replies
8
Views
5K
Find the maximum amplitude of the induced EMF
Replies
9
Views
7K
Standing wave transverse motion and amplitude
Replies
5
Views
2K
Wave equation, wavelenght not given
Replies
6
Views
2K
Conceptual Questions on a Mass Hanging from a Spring
Replies
2
Views
19K
Oscillating Spring Block System inside elevator
Replies
8
Views
5K
Finding the Phase Constant in a Mass/Spring System
Replies
2
Views
2K
Maximum compression of a spring?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top