Question

Figure shows the displacement-time graphs of two simple harmonic motions$ I$ and $II$. From the graph it follows that

• A. curve$ I$ has same frequency as that of curve $II$
• B. curve $I$ has frequency twice that of curve $II$
• C. curve $I$ has frequency half that of curve $II$
• D. curve $I$ has frequency four times that of curve $II$

Answer 1

Answer: (C)

From the graphs
For curve $I$,
Time period, $T_1 = 8\, s ,$
Frequency, $\upsilon_{1} = \frac{1}{T_{1}} = \frac{1}{8}Hz$
For curve $II$,
Time period, $T_ 2 = 4\, s$,
Frequency, $\upsilon_{2} = \frac{1}{T_{2}} = \frac{1}{4}Hz$
Their corresponding ratio
$\frac{\upsilon_{1}}{\upsilon_{2}} = \frac{1}{2}$ or $\upsilon_{1} = \frac{1}{2} \upsilon_{2}$