what is the peiod of vibrating object which an acceleration of 8.0m/s .when its displacement is 1.0m?what should be the answer?
a 10lb block of iron is caused to vibrate ith SHM by means of a spring.if the amplitude of vibrationis 12in and the time of complete vibration is 0.60s.Find the maximum kinetic energy of the block?
To calculate the period of a vibrating object, we need to know the acceleration and displacement.
The formula to calculate the period (T) is:
T = 2π√(d/a)
where:
T represents the period,
π is a mathematical constant equal to approximately 3.14159,
d represents the displacement, and
a represents the acceleration.
Given that the acceleration (a) is 8.0 m/s^2 and the displacement (d) is 1.0 m, we can substitute these values into the formula to find the period of the object.
T = 2π√(1.0 m / 8.0 m/s^2)
T = 2π√(0.125 s^2/m)
T = 2π * √(0.125) s
T ≈ 2π * 0.354 s
T ≈ 2.22 s
Therefore, the period of the vibrating object, with an acceleration of 8.0 m/s^2 and a displacement of 1.0 m, is approximately 2.22 seconds.
To find the period of a vibrating object, we need to determine the relationship between acceleration and displacement.
The formula that describes the relationship between acceleration, displacement, and period is:
a = (4π^2 * d) / T^2
where:
a is the acceleration
d is the displacement
T is the period
Rearranging the formula to solve for the period T, we have:
T = 2π * √(d/a)
Given:
a = 8.0 m/s^2
d = 1.0 m
Substituting the given values into the formula, we can calculate the period.
T = 2π * √(1.0 m / 8.0 m/s^2)
T = 2π * √(0.125 s^2/m)
Calculating further:
T ≈ 2π * 0.354 s
T ≈ 2.22 s
Therefore, the period of the vibrating object, with an acceleration of 8.0 m/s^2 and a displacement of 1.0 m, is approximately 2.22 seconds.