Question

SHM 4. Can velocity and acceleration reach maximal values during the simultaneously? Explain why! 5. A vertical spring with the spring constant 23,73 N/m is hanging from a ceiling. A small object with mass 1,103 kg is attached to the lower end of the spring, and the spring stretches to its equilibrium length. The object is then pulled down and released. The speed of the object when it is 4,985 cm from the equilibrium position is 0,4585 m/s. How far down was the object pulled?

Answer 1

Velocity and acceleration can never be maximum simultaneously in SHM

In case of an SHM, the motion is sinosoidal based and goverened by equations involving sine/cosine functions.

Eg:
y = y_o* sin(wt + p)
where w = angular frequency
p = phase constant
y = displacement

If we take the first derivative wrt time
y' = dy/dt = y_ow*cos(wt + p)

And y' is velocity of motion.

If we take the second derivative wrt time

y'' = d(dy/dt)/dt = -y_ow^2*sin(wt + p)

y''=Acceletation

When acceleration of y reaches maximum value when
sin(wt + p) = 1
ie phase angle is pi/2 or (2n*pi + pi/2) where n = 0,1,2.....

in those values of phase angle, velocity = 0 as cos(wt + p) = 0.

So, velocity and acceleration can never be maximum simultaneously in SHM

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