Question

Which of the following quantities are always zero in a simple harmonic motion?
(a) $\overrightarrow{F}\times \overrightarrow{a}.$

(b) $\overrightarrow{v}\times \overrightarrow{r}.$

(c) $\overrightarrow{a}\times \overrightarrow{r}.$

(d) $\overrightarrow{F}\times \overrightarrow{r}.$

Answer 1

$$\begin{gathered} \left(a\right)\stackrel{\rightharpoonup }{F}x\stackrel{\rightharpoonup }{a} \\ \left(b\right)\stackrel{\rightharpoonup }{v}x\stackrel{\rightharpoonup }{\stackrel{\rightharpoonup }{r}} \\ \left(c\right)\stackrel{\rightharpoonup }{a}x\stackrel{\rightharpoonup }{r} \\ \left(d\right)\stackrel{\rightharpoonup }{F}x\stackrel{\rightharpoonup }{r} \end{gathered}$$

As $\stackrel{\rightharpoonup }{F},\stackrel{\rightharpoonup }{a},\stackrel{\rightharpoonup }{r}and\stackrel{\rightharpoonup }{v}$ are either parallel or anti-parallel to each other, their cross products will always be zero.