A block of mass 1 kg is attached to a spring of force constant  .It is pulled 0.3 m from its equilibrium position and released from rest. This spring‐block apparatus is submerged in a viscous fluid medium which exerts a damping force of – 4 v (where v is the instantaneous velocity of the block). Determine of the position x(t) of the block at time t. 

Newton’s Law of Cooling states that the rate at which the object's temperature decreases is directly proportional to the difference between the temperature of the object and the ambient temperature. A cup of tea (temperature = 90°C) is placed in a room whose temperature is 30°C. After five minutes, the temperature of the tea has dropped to 70°C. After how much time would the temperature of the tea be 50°C?

Solve the following ordinary differential equations:

i) 

ii) 

iii) 

Consider two cylindrical pipes of equal length. One of these acts as a closed organ pipe and the other as open organ pipe. The frequency of the third harmonic in the closed pipe is 200 Hz higher than the first harmonic of the open pipe. Calculate the fundamental frequency of the closed pipe.

A stretched string of mass 20 g vibrates with a frequency of 30 Hz in its fundamental mode and the supports are 40 cm apart. The amplitude of vibrations at the antinode is 4 cm. Calculate the velocity of propagation of the wave in the string as well as the tension in it.

Design an astable multivibrator using IC 555 timer to generate a rectangular wave of 60% duty cycle at 10 kHz frequency

State the main subsystems of a CRO and explain their functions.

The linear density of a vibrating string is 1.3 × 10⁻⁴ kg m⁻¹. A transverse wave is propagating on the string and is described by the equation

y(x,t)=0.021 sin (30t - x)

where x and y are in metres and t is in seconds.

Calculate the tension in the string.

Explain the terms CMRR and input offset voltage in case of op-amp. 

A sinusoidal wave is described by

y(x,t) = 3.0 sin (3.52t - 2.01x)cm

where x is the position along the wave propagation. Determine the amplitude, wave number, wavelength, frequency and velocity of the wave.

The oscillations of two points x₁ and x₂ at x = 0 and x = 1 m respectively are modelled as follows:

y1 = 0.3 sin 4t

and  y2 = 0.3 sin (4t + /8)

Calculate the wavelength and speed of the associated wave.

Design and draw the circuit of a three channel op-amp adder with channel gains of -5, -10 and -15 respectively.

Establish the equation of motion of a weakly damped forced oscillator explaining the significance of each term. Differentiate between transient and steady state of the oscillator.

Draw a circuit of a non-inverting amplifier with gain 1 using op-amp. Draw the output voltage curve of this circuit for a step input of 5V amplitude and 50 kHz frequency, if the slew rate of the op-amp is 0.5 V/s. (Use proper scale on the time axis to illustrate the effect of slew rate).

For a damped harmonic oscillator, the equation of motion is

with m = 0.50 kg, = 0.70 kgs⁻¹ and k = 70 Nm⁻¹. Calculate (i) the period of motion, (ii) number of oscillations in which its amplitude will become half of its initial value, (iii) the number of oscillations in which its mechanical energy will drop to half of its initial value, (iv) its relaxation time, and (v) quality factor.

Design and draw a circuit of series pass voltage regulator to provide 25 V output voltage and 160 mA maximum load current using a silicon n-p-n transistor with =80. Assume the input unregulated voltage to be 30 V and minimum zener diode current to be 10 mA. Specify the voltage and power rating of zener diode as well as value and power rating of the resistor used.

Two collinear harmonic oscillations x₁ = 8 sin (100 πt) and x₂ = 12 sin (96 πt) are superposed. Calculate the values of time when the amplitude of the resultant oscillation will be (i) maximum and (ii) minimum.

In a voltage regulator circuit, the output voltage under no load condition is 12V while under full load it is 11.8V. Over the full range of input voltage variation the nominal voltage output of 12V varies by 50 mV. Calculate percentage load and line regulation.

State the Barkhausen criterion for sustained oscillations. Explain the operation of Colpitt Oscillator. For a Colpitt oscillator with 10 MHz frequency determine the equivalent capacitance, C forming tank circuit with 0.1 mH inductor.

The time period of a simple pendulum, called ‘seconds pendulum’, is 2 s. Calculate the length, angular frequency and frequency of the pendulum. What is the difference between a simple pendulum and a compound pendulum ?