search
Log In
0 votes

A spring mass damper system (mass $m$, stiffness $k$, and damping coefficient $c$) excited by a force $F(t) = B \sin w t$, where $B$, $w$ and $t$ are the amplitude, frequency and time, respectively, is shown in the figure. Four different responses of the system (marked as $\text{(i)}$ to $\text{(iv)}$) are shown just to the right of the system figure. In the figures of the responses, $A$ is the amplitude of response shown in red color and the dashed lines indicate its envelope. The responses represent only the qualitative trend and those are not drawn to any specific scale.

Four different parameter and forcing conditions are mentioned below.

$(P)$ $c>0$ and $w = \sqrt{k/m}$

$(Q)$ $c<0$ and $w \neq 0$

$(R)$  $c=0$ and $w = \sqrt{k/m}$

$(S)$ $c=0$ and $w \cong \sqrt{k/m}$

Which one of the following options gives correct match (indicated by arrow $\rightarrow$) of the parameter and forcing conditions to the response?

  1. $(P) \rightarrow \text{(i)}, (Q) \rightarrow \text{(iii)}, (R) \rightarrow \text{(iv)}, (S) \rightarrow \text{(ii)}$
  2. $(P) \rightarrow \text{(ii)}, (Q) \rightarrow \text{(iii)}, (R) \rightarrow \text{(iv)}, (S) \rightarrow \text{(i)}$
  3. $(P) \rightarrow \text{(i)}, (Q) \rightarrow \text{(iv)}, (R) \rightarrow \text{(ii)}, (S) \rightarrow \text{(iii)}$
  4. $(P) \rightarrow \text{(iii)}, (Q) \rightarrow \text{(iv)}, (R) \rightarrow \text{(ii)}, (S) \rightarrow \text{(i)}$
in Others 27.4k points
edited by

Please log in or register to answer this question.

Answer:

Related questions

0 votes
0 answers
$F(t)$ is a periodic square wave function as shown. It takes only two values, $4$ and $0$, and stays at each of these values for $1$ second before changing. What is the constant term in the Fourier series expansion of $F(t)$? $1$ $2$ $3$ $4$
asked Feb 15 in Others Arjun 27.4k points
0 votes
0 answers
Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point $(1, 2, 3)$. The surface integral $\int _{A} \vec{F}.d\vec{A}$ of a vector field $\vec{F} = 3x\hat{i} + 5y\hat{j} + 6z\hat{k}$ over the entire surface $A$ of the cube is _____________. $14$ $27$ $28$ $31$
asked Feb 15 in Others Arjun 27.4k points
0 votes
0 answers
Consider the definite integral $\int_{1}^{2} \left ( 4x^{2} + 2x + 6 \right )dx.$ Let $I_{e}$ be the exact value of the integral. If the same integral is estimated using Simpson’s rule with $10$ equal subintervals, the value is $I_{S}$. The percentage error is defined as $e = 100\times \left ( I_{e} - I_{S}\right )/I_{e}$. The value of $e$ is $2.5$ $3.5$ $1.2$ $0$
asked Feb 15 in Others Arjun 27.4k points
0 votes
0 answers
Given $\int_{-\infty }^{\infty } e^{-x^{2}} dx = \sqrt{\pi }.$ If $a$ and $b$ are positive integers, the value of $\int_{-\infty }^{\infty } e^{-a\left ( x+b \right )^{2}} dx$ is _______________. $\sqrt{\pi a}$ $\sqrt{\frac{\pi }{a}}$ $b\sqrt{\pi a}$ $b\sqrt{\frac{\pi }{a}}$
asked Feb 15 in Others Arjun 27.4k points
0 votes
0 answers
A polynomial $\varphi \left ( s \right ) = a_{n}s^{n} + a_{n-1}s^{n-1} + \cdots + a_{1}s+a_{0}$ of degree $n>3$ with constant real coefficients $a_{n}, a_{n-1}, \:\dots a_{0}$ has triple roots at $s = -\sigma$ ... $\varphi \left ( s \right ) = 0,$ and $\frac{d^{3}\varphi \left ( s \right )}{ds^{3}} = 0$ at $s = -\sigma$
asked Feb 15 in Others Arjun 27.4k points
...