Question

A mass is suspended from a vertical spring which is executing S.H.M. of frequency 5 Hz. The spring is unstretched at the highest point of oscillation. Maximum speed of the mass is ______. [acceleration due to gravity g = 10 m/s²]

Options

• 2π m/s

• π m/s

• `1/(2pi)` m/s

• `1/pi` m/s

Answer 1

A mass is suspended from a vertical spring which is executing S.H.M. of frequency 5 Hz. The spring is unstretched at the highest point of oscillation. Maximum speed of the mass is `underlinebb(1/pi)` m/s. [acceleration due to gravity g = 10 m/s²]

Explanation:

Time period, T = 2π`sqrt("m"/"k")`

and, frequency, n = `1/"T"=1/(2pi)sqrt("k"/"m")`

25 = `1/(4pi^2)"k"/"m"` ⇒ k = 100 π²m

kA = mg ⇒ A = `"mg"/"k"`

V_max = ωA = `(2pi)/"T"`A = 2πnA

= `(2pi5xx"mg")/"k"=(10pixx"m"xx10)/(100pi^2"m")=1/pi`