1. 0.42 Hz
The frequency of a simple harmonic motion for a spring is given by:

where 
k = 7 N/m is the spring constant 
m = 1 kg is the mass attached to the spring 
Substituting these numbers into the formula, we find

2. 2.38 s
The period of the harmonic motion is equal to the reciprocal of the frequency:

where f = 0.42 Hz is the frequency. Substituting into the formula, we find

3. 0.4 m
The amplitude in a simple harmonic motion corresponds to the maximum displacement of the mass-spring system. In this case, the mass is initially displaced by 0.4 m: this means that during its oscillation later, the displacement cannot be larger than this value (otherwise energy conservation would be violated). Therefore, this represents the maximum displacement of the mass-spring system, so it corresponds to the amplitude.
4. 0.19 m
We can solve this part of the problem by using the law of conservation of energy. In fact:
- When the mass is released from equilibrium position, the compression/stretching of the spring is zero:  , so the elastic potential energy is zero, and all the mechanical energy of the system is just equal to the kinetic energy of the mass:
, so the elastic potential energy is zero, and all the mechanical energy of the system is just equal to the kinetic energy of the mass:

where m = 1 kg and v = 0.5 m/s is the initial velocity of the mass
- When the spring reaches the maximum compression/stretching (x=A=amplitude), the velocity of the system is zero, so the kinetic energy is zero, and all the mechanical energy is just elastic potential energy:

Since the total energy must be conserved, we have:

5. Amplitude of the motion: 0.44 m
We can use again the law of conservation of energy.
-  is the initial mechanical energy of the system, with
 is the initial mechanical energy of the system, with  being the initial displacement of the mass and
 being the initial displacement of the mass and  being the initial velocity
 being the initial velocity
 is the mechanical energy of the system when x=A (maximum displacement)
 is the mechanical energy of the system when x=A (maximum displacement)
Equalizing the two expressions, we can solve to find A, the amplitude:

6. Maximum velocity: 1.17 m/s
We can use again the law of conservation of energy.
-  is the initial mechanical energy of the system, with
 is the initial mechanical energy of the system, with  being the initial displacement of the mass and
 being the initial displacement of the mass and  being the initial velocity
 being the initial velocity
 is the mechanical energy of the system when x=0, which is when the system has maximum velocity,
 is the mechanical energy of the system when x=0, which is when the system has maximum velocity, 
Equalizing the two expressions, we can solve to find  , the maximum velocity:
, the maximum velocity:
