Vibration Question: BoB Released from Rest, Solve for Theta & Vel/Acc at 1.6s

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The discussion focuses on solving a physics problem involving a pendulum released from rest, requiring the calculation of the angle theta, velocity, and acceleration after 1.6 seconds. Participants clarify the role of parameters such as amplitude (A), angular frequency (ω), and phase (φ) in the equation θ = A sin(ωt + φ). The importance of determining the period to find ω and the initial conditions to establish φ is emphasized. Questions arise about the need for derivatives to find velocity and acceleration. The conversation aims to guide the user through the necessary steps to solve the problem effectively.
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Homework Statement

:[/B]

BoB released from rest, L = 102 cm, theta = +-5 degrees, g = 9.81 m/s2
assume a SHM
(I) Determine the angle theta after 1.6 s
(II) Determine the magnitudes of velocity & acceleration of the BoB at 1.6 s

Homework Equations



theta = A sin (w t + phai)

The Attempt at a Solution



Does phai represent the period? And how do I get it?
Do I derive theta once & twice? And why?
How do I get w & A?

Thank you!
 
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Welcome to PF!

Hi FChebli! Welcome to PF! :smile:

(have a theta: θ and a phi: φ and an omega: ω :wink:)

θ = A sin(ωt + φ)

A is the maximum value (θ varies between ±A), which you can find from the question

ω is the frequency … to find the period, you need the value of t which makes (ωt + φ) increase by 2π

φ is the phase … it's often zero, but not always … you find it by putting t = 0, and seeing what θ is (or dθ/dt, if that's given instead) :wink:
 
Thank you so much! :)
 
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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