The displacement of a particle in simple harmonic motion is given by:
\[
x = A_0 \cos \left( \frac{\pi}{2} t \right)
\]
The distance traveled by the particle in the interval between \( t = 2 \) and \( t = 5 \) seconds and its position at \( t = 5 \) second are:
Show Hint
- \( A_0 \) and mean position
- \( A_0 \) and extreme position
- \( 3 A_0 \) and mean position
- \( 3 A_0 \) and extreme position
The Correct Option is C
Solution and Explanation
Step 1: Understanding the SHM Equation
- The given displacement equation follows: \[ x = A_0 \cos \left( \frac{\pi}{2} t \right) \] - The amplitude of oscillation is \( A_0 \).
Step 2: Finding the Distance Traveled from \( t = 2 \) to \( t = 5 \)
- At \( t = 2 \): \[ x_2 = A_0 \cos \left( \frac{\pi}{2} \times 2 \right) = A_0 \cos (\pi) = -A_0 \] - At \( t = 5 \): \[ x_5 = A_0 \cos \left( \frac{\pi}{2} \times 5 \right) = A_0 \cos \left( \frac{5\pi}{2} \right) = 0 \] - The particle moves from \( -A_0 \) (extreme) → 0 → \( +A_0 \) (extreme) → 0 (mean position). - Total distance traveled = \( A_0 + 2 A_0 = 3 A_0 \).
Step 3: Finding the Final Position
- At \( t = 5 \), \( x_5 = 0 \), which means the particle is at the mean position.
Step 4: Conclusion
Since the total distance traveled is \( 3A_0 \) and the final position is the mean position, Option (3) is correct.
Top TS EAMCET Physics Questions
- A wooden box lying at rest on an inclined surface of a wet wood is held at static equilibrium by a constant force $F$ applied perpendicular to the incline. If the mass of the box is $1\,kg$, the angle of inclination is $30^{\circ}$ and the coefficient of static friction between the box and the inclined plane is $0.2$, the minimum magnitude of $\vec{F}$ is (Use $ g = 10\,m/s^2$)
- A metre scale made of steel reads accurately at $25^{\circ} C$ . Suppose in an experiment an accuracy of $0.06\, mm$ in $1\,m$ is required, the range of temperature in which the experiment can be performed with this metre scale is (coefficient of linear expansion of steel is $ 11 \times 10^{-6} /^{\circ} \, C$ )
- Consider a solenoid carrying current supplied by a DC source with a constant emf containing iron core inside it. When the core is pulled out of the solenoid, the change in current will
- A parallel beam of light of intensity \(I_0\) is incident on a coated glass plate. If \(25\%\) of the incident light is reflected from the upper surface and \(50\%\) of light is reflected from the lower surface of the glass plate, the ratio of maximum to minimum intensity in the interference region of the reflected light is
- A thermocol box has a total wall area (including the lid) of $1.0 m ^{2}$ and wall thickness of $3 cm$. It is filled with ice at $0^{\circ} C$. If the average temperature outside the box is $30^{\circ} C$ throughout the day, the amount of ice that melts in one day is [Use $K_{\text {thermocol }}=0.03 W / mK$ $.L_{\text {fusion (ice) }}=3.00 \times 10^{5} J / kg ]$
Top TS EAMCET laws of motion Questions
- A block of mass $10 \,kg$, initially at rest, makes a downward motion on $45^{\circ}$ inclined plane. Then the distance travelled by the block after $2 s$ is (Assume the coefficient of kinetic friction to be $0.3$ and $g=10\, ms ^{-2} )$
A player can throw a ball to a maximum horizontal distance of 80 m. If he throws the ball vertically with the same velocity, then the maximum height reached by the ball is:
If a man of mass 50 kg is in a lift moving down with a acceleration equal to acceleration due to gravity, then the apparent weight of the man is:
A ball falls freely from a height h on a rigid horizontal plane. If the coefficient of resolution is e, then the total distance travelled by the ball before hitting the plane second time is:
A man weighing 75 kg is standing in a lift. The weight of the man standing on a weighing machine kept in the lift when the lift is moving downwards freely under gravity is:
Top TS EAMCET Questions
- A bag contains $5$ red balls, $3$ black balls and $4$ white balls are drawn at random. The probability that they are not of same colour is
- If $cosec\, \theta - \cot \theta = 2017$, then quadrant in which $\theta $ lies is
- If $a$ is a unit vector, then $| a \times \hat{ i }|^{2}+| a \times \hat{ j }|^{2}+| a \times \hat{ k }|^{2}=$
- $A$ straight line makes an intercept on the $Y$-axis twice as long as that on $X$-axis and is at a unit distance from the origin. Then the line is represented by the equations
- Let $S$ and $S'$ be the foci of an ellipse and B be one end of its minor axis. If $SBS'$ is an isosceles right angled triangle then the eccentricity of the ellipse is