mn x +3.0 cm. A mass m 450 g is attached to an ideal, massless spring (k 85 N/m)

Question

mn x +3.0 cm. A mass m 450 g is attached to an ideal, massless spring (k 85 N/m), as shown above. The surface is frictionless. The mass is initially pulled aside to a displacement of x +3.0 cm. The mass is then released from rest and allowed to oscillate freely 25. (2 pts.) What is the frequency of the oscillations? A. 0.55 Hz D. 2.2 Hz E. 2.9 Hz B. 0.79 Hz C. 1.3 Hz 26. (2 pts.) What is the greatest acceleration that the mass experiences during its oscillation? A. 2.6 m/s D. 7.0 m/s B. 4.0 m/s E. 9.8 m/s2 C. 5.7 m/s 27. (2 pts.) What is the total mechanical energy of the system? A. 0.038 J D. 0.25 J B. 0.095 J E. 0.41 J C. 0.13 J

Explanation / Answer

Here ,

mass of block , m = 0.450 Kg

spring constant , k = 85 N/m

initial displacement , ampitude , A = 3 cm = 0.03 m

28)

frequency = sqrt(k/m)/2pi

frequency = 2.2 Hz

the frequency is 2.2 Hz

26)

maximum acceleration , a = A*(2*pi*f)^2

maximum acceleration , a = 0.03 * (2.2 * 6.282)^2

maximum acceleration , a = 5.7 m/s^2

the maximum acceleration of the block is 5.7 m/s^2

27)

total mechanical energy = 0.5 * k*A^2

total mechanical energy = 0.5 * 85 * 0.03^2

total mechanical energy = 0.0383 J

the total mechanical energy is 0.0383 J

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