Calculating Position and Distance in Simple Harmonic Motion: A Case Study

AI Thread Summary
The discussion revolves around calculating the position and distance of an object in simple harmonic motion after being released from rest. The user derived the spring constant using the equation -ky - mg = 0 and formulated the position equation as x(t) = 0.18cos(5.29t). They inquired about the object's position at 84.4 seconds and the distance traveled, clarifying the difference between distance and displacement. The response highlighted that for each complete oscillation, the distance traveled is four times the amplitude, and the user acknowledged a mistake regarding double posting. The conversation emphasizes the importance of understanding both distance and displacement in harmonic motion calculations.
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Hi, I would really like to know if my solution to the following question is correct, I would really really really appreciate it.

A hanging spring stretches by 35cm when an object of mass 450g is hung on it at rest. In this situation, we define its position as x=0. The object is pulled down an additional 18cm and released from rest to oscillate without friction. What is its position x at a time 84.4s later?
Find the distance traveled by the vibrating object.


Well, by using the equation -ky-mg=0 (at rest) I derived the equation
y=-mg/k. So i replaced y with 35 cm and m with 0.45kg in order to find k.
With k, i set the equation: x(t)= Acos(wt+c) c=phase constant w=angular frequency
and since this started at rest, there is no phase constant, and amplitude is 18cm so i made the equation
x(t)=0.18cos(5.29t)
then i replace the t with 84.4. Is this right?
And I'm having problems finding the distance traveled by the vibrating object.
Thanks a lot. And please, help! :confused:
 
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You want distance traveled not displacement, right?

During the given time how many complete oscillations. For each complete oscillation the distance traveled is 0.18 x 4 m.
 
Thank you so much. But i have another question, how do you find the displacement?
and did i answer the question itself correctly?
 
The magnitude of the displacement is the distance between the final and initial position, no matter how many full oscillations are completed.

May you please explain the double posting?
 
Last edited:
Sorry about that

Yes, I'm sorry i didn't know that double posting was not permitted on this forum, i sincerely apologize for violating that rule as this will never happen again. And thank you very much for assisting me and pointing that out for me. Greatly appreciate it.
 
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}...
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