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?

Question

<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? (A) 0.05 m (B) 0.10 m (C) 0.20 m (D) 0.707 m

Tardigrade Admin · Accepted Answer

k eq =70 N / m m =0.7 kg ω=√( k cq / m ) ω=10 v max = A ω 1= A × 10 A =0.1 m

0.05 m

0.10 m

0.20 m

0.707 m

keq​=70N/m m=0.7kg ω=mkcq​​​ ω=10 vmax​=Aω 1=A×10 A=0.1m

$k_{e q} = 70 N / m$
$m = 0.7 k g$
$ω = \frac{k _{c q}}{m}$
$ω = 10$
$v_{m a x} = A ω$
$1 = A \times 10$
$A = 0.1 m$