Home
Class 11
PHYSICS
A 3 kg collar attached to a spring of fo...

A 3 kg collar attached to a spring of force constant `1200 Nm^(-1)` slides without friction on a horizontal rod. The collar is displaced from its equilibrium position by 6.0 cm and released. Calculate (a) the period of oscillation, (b) the maximum magnitude of acceleration and (c) the maximum speed of collar. (Fig)

Text Solution

Verified by Experts

`m = 3 kg , k = 1200 Nm^(-1)`
Amplitude `= a = 6 xx10^(-2)m`
`T=2pisqrt(m/k)=2xx3.14 sqrt(3/(1200))=0.314s`
Maximum acceleration `a_(max)=aomega^2=(ak)/m`
`= 6xx10^(-2)xx1200/3=24ms^(-2)`
Maximum Speed `=v_(max)=aomega`
`6xx10^(-2)xxsqrt(k/m)=6xx10^(-2)sqrt((1200)/3)=0.120 ms^(-1)`
Promotional Banner

Topper's Solved these Questions

  • OSCILLATIONS

    ICSE|Exercise SHORT ANSWER QUESTIONS WITH ANSWER|20 Videos

  • OSCILLATIONS

    ICSE|Exercise LONG ANSWER QUESTIONS |3 Videos

  • OSCILLATIONS

    ICSE|Exercise SELECTED PROBLEMS (OSCILLATION IN A TUNNEL BORED THROUGH THE EARTH)|2 Videos

  • MOTION IN FLUIDS

    ICSE|Exercise SELECTED PROBLEMS (FROM POISEUILLE.S FORMULA) |19 Videos

  • PROPERTIES OF MATTER

    ICSE|Exercise MODULE 4 ( TEMPERATURE ) UNSOLVED PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

A 2.5 kg collar attached to a spring of foce constant 1000 Nm^(-1) slides without friction on a horizontal rod. The collar is displaced from its equilibrium position by 5.0 cm and released. Calculate (i) the period of oscillation (ii) the maximum speed of the collar and (iii) the maximum acceleration of the collar.

A 5 kg collar is attached to a spring of spring constant 500 N m^(-1) . It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by 10 cm and released. The time period of oscillation is

A 5 kg collar is attached to a spring of spring constant 500 Nm^(-1) . It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by 10 cm and released. Calculate (a) The period of oscillations (b) The maximum speed and (c) maximum acceleration of the collar.

A 2.5 kg collar is attached to a spring of spring constant 250 Nm^(-1) . It slides without friction over a horizontal surface . It is displaced from its equilibrium position by 20 cm and releasd. Calculate the period of osciallation and the maximum speed.

A 10 kg collar is attached to a spring of spring constant 1000 Nm^(-1) . It slides without friction over a horizontal surface. If is displaced from its equilibrium position by 20 cm and released . Calculate (a) The period of oscillation (b) The maximum speed Hint : T= 2pi sqrt((m)/(k)) , v_(m) = A omega = A sqrt((k)/(m))

A 5kg collar is attached to a spring . It slides without friction over a horizontal surface. It is displaced from its equilibrium position by 10 cm and released , its maximum speed is 1 ms^(-1) Calculate (a) Spring constant (b) The period of oscillation (c ) Maximum acceleration of the collar Hint : m = 5 kg , A= 0.1 m ,k =?, T =? or a=? , v_(m) =1 ms^(-1) v_(m) = Aomega =A sqrt((k)/(m)) Find k, T = 2pi sqrt((m)/(k)) a_(max) = omega^(2) A = (k)/(m) A

A mass of 1.5 kg is connected to two identical springs each of force constant 300 Nm^(-1) as shown in the figure. If the mass is displaced from its equilibrium position by 10cm, then the period of oscillation is

A trolley of mass 3.0kg is connected to two identical spring each of force constant 600Nm^(-1) as shown in figure. If the trolley is displaced from its equilibrium position by 5.0 cm and released, what is (a) the period of ensuing oscillation? (b) the maximum speed of trolley? (c) How much is the total energy dissipated as heat by the time the trolley comes to rest due to damping forces?

A mass of 1.5 kg is connected to two identical springs each of force constant 300 Nm^(-1) as shown in the figure. If the mass is displaced from its equilibrium position by 10 cm, then maximum speed of the trolley is

A 4 kg roller is attached to a massless spring of spring constant k = 100 N/m. It rolls without slipping along a frcitionless horizontal road. The roller is displaced from its equilibrium position by 10 cm and then released. It rolls without slipping along a frictionless horizontal road. The roller is displaced from its equilibrium position by 10 cm and then released. Its maximum speed will be