Determine Speed & Acceleration of Spring Motion

  • Thread starter Thread starter mikefitz
  • Start date Start date
  • Tags Tags
    Motion Spring
AI Thread Summary
To determine the speed and acceleration of an object in simple harmonic motion, the first and second derivatives of the displacement function x(t) with respect to time are essential. The first derivative gives the speed of the object, while the second derivative provides the acceleration. For the given values of amplitude (A = 0.087 m) and period (T = 1.8 s), these derivatives can be calculated using the appropriate mathematical formulas. Users are encouraged to reference physics or calculus resources for further clarification on these concepts. Understanding these derivatives is crucial for solving the problem effectively.
mikefitz
Messages
155
Reaction score
0
An 0.64-kg object is attached to one end of a spring, as in Fig. 10.14 and the system is set into simple harmonic motion. The displacement x of the object as a function of time is shown in the drawing above. Please take the values of A and T as: A = 0.087 m and T = 1.8 s. With the aid of this data, determine


ive already calculated amplitude, angular frequency, spring constant.

I can't figure out how to calculate these:

(d) the speed of the object at t = 3.6 s

(e) and the magnitude of the object's acceleration at t = 3.6 s


any tips??
 
Physics news on Phys.org
You have a function x(t) which represents displacement. Now, what do the first and second derivatives of this function with respect to time represent?
 
sorry but I'm really lost here - can you please clarify what you mean by what the first and second derivatives with respect to time means? thanks for your patience
 
mikefitz said:
sorry but I'm really lost here - can you please clarify what you mean by what the first and second derivatives with respect to time means? thanks for your patience

I don't want to sound uncooperative, but I think you should do some google-ing at this point or consult your physics/calculus books.
 
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 »

Similar threads

Damped harmonic motion
Replies
3
Views
651
Distribution of Energy when work is done on a system of 2 masses connected by a spring
Replies
17
Views
2K
Stretched spring attached to the center of a pure rolling disk
Replies
11
Views
1K
Initial velocity of bird landing on horizontal wire modeled as spring
Replies
7
Views
974
Maximum speed and magnitude of the acceleration of a spring?
Replies
4
Views
2K
Simple Harmonic Motion of a Spring?
Replies
11
Views
2K
Solve Spring Force Problem: Displacement, Velocity & Acceleration
Replies
6
Views
2K
Two spring-coupled masses in an electric field (one of the masses is charged)
Replies
1
Views
913
What Is the Spring Constant in This Simple Harmonic Motion Problem?
Replies
2
Views
7K
Elastic potential energy (spring) problem
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top