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$2x^{}+c{x}^{}+5x=0,$

where $c$ is a constant capturing the effect due to damping. Assume an initial displacement of $1,3$ and the mass is released from rest.

$5($a$)$ Pick an integer for the value of $c$ so the system oscillates.

$\frac{10}{{15}^{(b)}}$ With your choice made $in(a),$ obtain the solution $to$ the above equation.

$($c$)$ Sketch the displacement of the mass as a function of time $t.$