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  4. <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/467bb986bf54a06eed0ffed01fa9405d-.png /> A device used to print large maps, drawings, graphs, etc. is known as plotter. A plotter contains a printing head and a drum through which the paper comes out. The plotting pencil is held in a block which in turn is held by a system of four springs as shown. The spring constants of the four springs are k 1=20 N / m , k 2=30 N / m , k 3=60 N / m and k 4=30 N / m Initially, the pencil is in the middle, i.e. at x=0 and all the springs are in natural length. The velocity of paper coming out is v 0=0.2 m / s. The block is set up in motion by giving a velocity v = 1 m / s towards right. The mass of the pencil block with pencil is m 1=0.7 kg. The friction is assumed to be absent in the system. What is the value of the amplitude A?

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A device used to print large maps, drawings, graphs, etc. is known as plotter. A plotter contains a printing head and a drum through which the paper comes out.
The plotting pencil is held in a block which in turn is held by a system of four springs as shown.
The spring constants of the four springs are $k _{1}=20\, N / m , k _{2}=30 \,N / m , k _{3}=60 \,N / m$ and $k _{4}=30\, N / m$
Initially, the pencil is in the middle, i.e. at $x=0$ and all the springs are in natural length.
The velocity of paper coming out is $v _{0}=0.2 \,m / s$. The block is set up in motion by giving a velocity $v =$ $1 \,m / s$ towards right.
The mass of the pencil block with pencil is $m _{1}=0.7\, kg$.
The friction is assumed to be absent in the system.
What is the value of the amplitude $A$?

Oscillations

Solution:

$k _{ eq }=70 N / m$
$m =0.7\, kg$
$\omega=\sqrt{\frac{ k _{ cq }}{ m }}$
$\omega=10$
$v _{\max }= A \omega$
$1= A \times 10$
$A =0.1 \,m$