Question 139: Oscillations

Question

Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures. 
x(t) = A sin (at + $$\delta $$)
y(t) = B sin (bt)
Identify the correct  match below.

Accepted Answer

The given simple harmonic motions to form Lissajous figures are $$x(t) = A\sin (at + \delta )$$ and $$y(t) = B\sin (bt)$$.
For parabola, conditions should be
A = B or A $$
e$$ B, a = 2b, $$\delta$$ = $$\pi$$/2
For line, conditions should be
A = B, a = b, $$\delta$$ = $$\pi$$
For circle, condition should be
A = B, a = b; $$\delta$$ = $$\pi$$/2
For ellipse, condition should be
A $$
e$$ B, a = b; $$\delta$$ = $$\pi$$/2
Therefore, we obtain an ellipse.

Answer

Parameters   A $$ 
e $$ B, a = b; $$\delta $$ = 0;
Curve    Parabola

Answer

Parameters    A = B, a = b; $$\delta $$ = $${\raise0.5ex\hbox{$\scriptstyle \pi $}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}$$
Curve    Line

Answer

Parameters    A $$ 
e $$ B, a = b; $$\delta $$ = $${aise0.5ex\hbox{$\scriptstyle \pi $}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}$$
Curve    Ellipse

Answer

Parameters    A = B,  a = 2b; $$\delta $$ = $${\raise0.5ex\hbox{$\scriptstyle \pi $}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}$$
Curve    Circle

Oscillations

Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures. x(t) = A sin (at + $\delta $) y(t) = B sin (bt) Identify the correct match below.

Choose the correct answer: