When a mass mm is suspended from a particular vertical spring, the spring stretches a distance dd from its natural length. For parts $($b$)$ and $($c$)$ below, take up to be the positive xx direction.

lhmpiii@outlook.com$6$C$65-37-$E$5-4$F$-$A$698-50894$

$$ Part $($a$)$

The mass is displaced from equilibrium and allowed to oscillate. What is the angular frequency of the motion in terms of given parameters and gg$?$

$-$ Part $($b$)$

If the mass is displaced upwardsupwards a distance AA and released from rest at time t$=0$t$=0,$ which of the equations below describes the resulting motion?

x$($t$)=$Acos$($t$)$x$($t$)=$Acos$($t$)$Correct$!$

$-$ Part $($c$)$

If the mass is displaced downwardsdownwards a distance AA and released from rest at time t$=0$t$=0,$ which of the equations below describes the resulting motion?

x$($t$)=$Acos$($t$+$$)$x$($t$)=$Acos$($t$+$$)$Correct$!$

$$ Part $($d$)$

Assuming the initial condition from part $($b$)($mass displaced upwards$),$ what is the smallest time greater than zero at which the mass is at equilibrium? Express in terms of given parameters.

tmin $=$

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