Which of the following quantities are always positive in a simple harmonic motion?

Question

Which of the following quantities are always positive in a simple harmonic motion? (A)  overset arrow F. overset arrow a (B)  overset arrow v. overset arrow r (C)  overset arrow a. overset arrow r (D)  overset arrow F. overset arrow r

Tardigrade Admin · Accepted Answer

For a simple harmonic motion, F=-kx,a=-(ω )2xandv=±√(A2 - x2) Now, overset arrow F. overset arrow a=(F)(a)cosθ ∵ (θ = 0 ° ) overset arrow F. overset arrow a=k(ω )2x2 Hence, overset arrow F. overset arrow a has a positive value.

Q. Which of the following quantities are always positive in a simple harmonic motion?

$F \to . a \to$

$v \to . r \to$

$a \to . r \to$

$F \to . r \to$

For a simple harmonic motion, $F = - k x, a = - (ω)^{2} x an d v = \pm (A^{2} - x^{2})$
Now,
$F \to . a \to = (F) (a) cos θ ∵ (θ = 0^{\circ}) F \to . a \to = k (ω)^{2} x^{2}$
Hence, $F \to . a \to$ has a positive value.

Q. Which of the following quantities are always positive in a simple harmonic motion?

F→.a→

v→.r→

a→.r→

F→.r→

For a simple harmonic motion, F=−kx,a=−(ω)2xandv=±(A2−x2)​ Now, F→.a→=(F)(a)cosθ∵(θ=0∘)F→.a→=k(ω)2x2 Hence, F→.a→ has a positive value.

$F \to . a \to$

$v \to . r \to$

$a \to . r \to$

$F \to . r \to$

For a simple harmonic motion, $F = - k x, a = - (ω)^{2} x an d v = \pm (A^{2} - x^{2})$
Now,
$F \to . a \to = (F) (a) cos θ ∵ (θ = 0^{\circ}) F \to . a \to = k (ω)^{2} x^{2}$
Hence, $F \to . a \to$ has a positive value.