Question

Which of the following quantities are always negative in a simple harmonic motion?
(a) →F. →a.
(b) →v. →r.
(c) →a. →r.
(d) →F. →r.

Answer 1

Answer:

dot product of displacement with force and displacement with acceleration always -ve in SHM....

Answer 2

Explanation:

In a simple harmonic motion, a⇀.r⇀ and F⇀.r⇀

So, negative value is always seen in $\vec{F} \cdot \vec{r}$. Just like the force, as the acceleration has the same direction, we can find negative value with $\vec{a} \cdot \vec{r}$ .

• Since acceleration and force is in displacement’s opposite direction, the displacement ‘s dot product of →r with a and →F  is continuously lesser than zero.  

• Acceleration and force are in same direction always. Thus, the dot product of a and F is always more than zero.

• Displacement and Velocity are not in the same direction always. So, the dot product of →r and v  is sometimes less than zero and sometimes greater than zero.