Derivation of an S.H.M. Equation

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To derive the equation for Simple Harmonic Motion (SHM), start by establishing the relationship between acceleration and displacement, noting that acceleration is directly proportional to the negative of displacement. Using Newton's second law (F=ma), express acceleration (a) in terms of displacement (x), leading to the equation a = -ω²x, where ω is the angular frequency. The angular frequency can be related to the period (T) by the formula ω = 2π/T, which can be rearranged to T = 2π/ω. This derivation connects mass (m) and spring constant (k) to the period of oscillation, resulting in T = 2π√(m/k). Understanding these relationships is crucial for modeling harmonic motion effectively.
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Can anybody show me how to derive the equation for SHM. (T = 2 x (Pie) x (root m/k))

Help would be greatly appreciated, as i need it for coursework
 
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No one will show you, but we will help you along it deriving it yourself.
How can you model harmonic motion? What function would you use?
 
it depends on cases. but I can give you the general way

first you should find the relationship between the acceleration of oscillator and its displacement

Then, by means of Newton's second law, F=ma
find the a in terms of x if a is directly proportional to minus x
then, for S.H.M a = -w^2x , where w is the angular frequency of motion
w = =2pi/T
T=2pi/w
 
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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