Proof of Periodic Sinusoidal waveforms

AI Thread Summary
To prove that the sinusoidal waveform x(t) = cos(2t + π/4) is periodic, one must demonstrate that x(t + T) = x(t) for some period T. The general property of cosine functions indicates they are periodic with a fundamental period of 2π, meaning the function will repeat its values every 2π. The phase shift does not affect the periodicity, so the waveform retains its periodic nature. The discussion highlights the relationship between the cosine function and its periodicity, suggesting that using the identity cos(A + 2πn) can aid in the proof. Understanding these properties is essential for confirming the periodicity of sinusoidal waveforms.
tomh
Messages
1
Reaction score
0

Homework Statement


Hi,

Have completely forgotten how to prove that a sinusoidal waveform is periodic and can't seem to find it anywhere. So was hoping someone could here.

I've got the signal x(t)=cos(2t+pi/4)

and am trying to prove it is periodic.

Homework Equations



wt=theta

f(x+k)=f(x)

cos(x)=sin(x+pi/2)

The Attempt at a Solution



I know that it is periodic, but to prove I think I have to prove that x(t)=0

Have tried letting t=-pi/8 but with the phase change of pi/2 to convert it to a sine again it gives me a non zero answer.

Anyone with any help would be greatly appreciated.
 
Physics news on Phys.org
welcome to pf!

hi tomh! welcome to pf! :smile:

(have a pi: π and a theta: θ :wink:)

cos(A + 2πn) = cosAcos2πn - sinAsin2πn = cosA

does that help?​
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanged mass'

Thread 'A cylinder connected to a hanged mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Fourier series, periodic function for a string free at each end
Replies
8
Views
2K
Superposition of two one-dimensional harmonic waves
Replies
10
Views
2K
Oscillatory motion equation in sine function
Replies
6
Views
3K
Harmonic Motion with External Force: Impact on Period?
Replies
3
Views
1K
Estimating damped harmonic oscillator parameters from this plot of the oscillations
Replies
9
Views
2K
How to calculate quality factor for RLC circuit?
Replies
6
Views
1K
Difference between resonance in undamped vs damped mass-spring-dashpot
Replies
17
Views
2K
Aliasing, Continuous sinusoids and discrete sinusoids....
Replies
3
Views
1K
Tension developed in a charged ring
Replies
2
Views
2K
Time Period of a Small Oscillation
Replies
26
Views
5K

Hot Threads

Recent Insights

Back
Top