The maximum acceleration of a particle in SHM is made two times keeping the maximum speed to be constant. It is possible when

Question

The maximum acceleration of a particle in SHM is made two times keeping the maximum speed to be constant. It is possible when (A) amplitude of oscillation is doubled while frequency remains constant (B) amplitude is doubled while frequency is halved (C) frequency is doubled while amplitude is halved (D) frequency is doubled while amplitude remains constant.

Tardigrade Admin · Accepted Answer

2 Ai ωi2=Af ωf2 Ai ωi=Af ωf If ωf=2 ωi and Af=(Ai/2) The condition will be satisfied.

Q. The maximum acceleration of a particle in SHM is made two times keeping the maximum speed to be constant. It is possible when

amplitude of oscillation is doubled while frequency remains constant

amplitude is doubled while frequency is halved

frequency is doubled while amplitude is halved

frequency is doubled while amplitude remains constant.

$2 A_{i} ω_{i}^{2} = A_{f} ω_{f}^{2}$
$A_{i} ω_{i} = A_{f} ω_{f}$
If $ω_{f} = 2 ω_{i}$ and $A_{f} = \frac{A _{i}}{2}$
The condition will be satisfied.

Q. The maximum acceleration of a particle in SHM is made two times keeping the maximum speed to be constant. It is possible when

amplitude of oscillation is doubled while frequency remains constant

amplitude is doubled while frequency is halved

frequency is doubled while amplitude is halved

frequency is doubled while amplitude remains constant.

2Ai​ωi2​=Af​ωf2​ Ai​ωi​=Af​ωf​ If ωf​=2ωi​ and Af​=2Ai​​ The condition will be satisfied.

$2 A_{i} ω_{i}^{2} = A_{f} ω_{f}^{2}$
$A_{i} ω_{i} = A_{f} ω_{f}$
If $ω_{f} = 2 ω_{i}$ and $A_{f} = \frac{A _{i}}{2}$
The condition will be satisfied.