Question

if
the maximum acceleration of a SHM is alpha and the maximum velocity is betathen amplitude of vibration is given by is a​

Answer 1

Answer:

Acceleration

Explanation:

Acceleration has a different story. At the middle (x = 0), acceleration is zero. At the extreme ends, when a spring is at its maximum stretch or compress, the spring force is at its maximum magnitude, and therefore the acceleration it gives to the attached mass is maximum.

Answer 2

Answer:

The amplitude of the vibration = β²/α

Explanation:

Given :

maximum acceleration = α

maximum velocity = β

To find :

the amplitude of vibration

Solution :

In SHM,

⇝ maximum acceleration = ω²A

     α = ω²A

⇝ maximum velocity = ωA

     β = ωA

where A is the amplitude of the vibration

Divide maximum acceleration by maximum velocity,

$\sf \dfrac{maximum \ acceleration}{maximum \ velocity}$

$\sf \dfrac{\alpha}{\beta} =\dfrac{\omega^2A}{\omega A}\\\\ \sf \dfrac{\alpha}{\beta}=\omega$

Substitute ω = α/β in maximum velocity formula,

  β = ωA

  β = (α/β) × A

  β² = αA

  A = β²/α

∴ The amplitude of the vibration = β²/α